SOCR - User contributions [en]

SOCR EduMaterials ExperimentsActivities

2006-10-27T15:55:35Z

Juanas:

== [http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials SOCR Educational Materials] - Experiments Activities ==

* [[SOCR_EduMaterials_Activities_DieCoin | SOCR Die Coin Experiment Activity]]
* [[SOCR_EduMaterials_Activities_CardsCoinsSampling | Cards & Coins Sampling Activity]]
* [[SOCR_EduMaterials_Activities_MontyHall | SOCR Monty Hall Experiment Activity]]
* [[SOCR_EduMaterials_Activities_DiceExperiment | SOCR Dice Experiment Activity]]
* [[SOCR_EduMaterials_Activities_CoinDieExperiment | SOCR Coin Die Experiment Activity]]
* [[SOCR_EduMaterials_Activities_Matching_Juana_oct10-06_version1 | SOCR Matching experiment Activity]]

<hr>
* SOCR Home page: http://www.socr.ucla.edu

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SOCR EduMaterials Activities Matching Juana oct10-06 version1

2006-10-27T15:40:13Z

Juanas:

Quite often, a method used to solve a problem in probability can be used to solve many other problems which at first glance appear different, but are conceptually the same. This exercise illustrates this.

Go to the matching experiment in SOCR http://socr.stat.ucla.edu/htmls/SOCR_Experiments.html
Run it several times and play with it until you feel comfortable with it. Then use it and interpret it appropriately to answer the following problems:

(1) Six students are working on a project for their Statistics class that requires a lot of calculations. Each of them is in charge of calculating one part of the project, but they all will share the results. As they work, they pass around their papers so that everyone can see the results of the others. The smoke alarm sounds suddenly and each student grabs the nearest paper and hurriedly leaves the room. What is the theoretical probability that none of the students took his or her paper? What is the probability that you obtain from the data generated after repeating the correct experiment 1000 times?
Attach a snapshot of the applet that shows how you found your answer with SOCR. (the snapshot should show the theoretical true probability and the probability you got by repeating this experiment 1000 times. Highlight what in the snapshot is your answer.

(2) 20 ladies arrive to a party and leave their coats with the concierge, who is not a very organized person. At the end of the party, the ladies don’t really remember what their coats look like (too much dancing and chocolate cake) and have lost the numbers the concierge give them. So the concierge has to give them the coats back at random. What is the theoretical probability that at least two ladies get their own coat? What is the probability that you obtain from the data generated after repeating the correct experiment 1000 times?
Attach a snapshot of the applet that shows how you found your answer with SOCR. (the snapshot should show the theoretical true probability and the probability you got by repeating (appropriately) this experiment 1000 times. Highlight what in the snapshot is your answer.

SOCR EduMaterials Activities Matching Juana oct10-06 version1

2006-10-27T15:38:41Z

Juanas:

Quite often, a method used to solve a problem in probability can be used to solve many other problems which at first glance appear different, but are conceptually the same. This exercise illustrates this.

Go to the matching experiment in SOCR http://socr.stat.ucla.edu/htmls/SOCR_Experiments.html
Run it several times and play with it until you feel comfortable with it. Then use it and interpret it appropriately to answer the following problems:

(1) Six students are working on a project for their Statistics class that requires a lot of calculations. Each of them is in charge of calculating one part of the project, but they all will share the results. As they work, they pass around the calculators so that everyone can see the results of the others. The smoke alarm sounds suddenly and each student grabs the nearest calculator and hurriedly leaves the room. What is the theoretical probability that none of the students too his or her calculator? What is the probability that you obtain from the data generated after repeating the correct experiment 1000 times?
Attach a snapshot of the applet that shows how you found your answer with SOCR. (the snapshot should show the theoretical true probability and the probability you got by repeating this experiment 1000 times. Highlight what in the snapshot is your answer.

(2) 20 ladies arrive to a party and leave their coats with the concierge, who is not a very organized person. At the end of the party, the ladies don’t really remember what their coats look like (too much dancing and chocolate cake) and have lost the numbers the concierge give them. So the concierge has to give them the coats back at random. What is the theoretical probability that at least two ladies get their own coat? What is the probability that you obtain from the data generated after repeating the correct experiment 1000 times?
Attach a snapshot of the applet that shows how you found your answer with SOCR. (the snapshot should show the theoretical true probability and the probability you got by repeating (appropriately) this experiment 1000 times. Highlight what in the snapshot is your answer.

SOCR EduMaterials Activities Matching Juana oct10-06 version1

2006-10-27T15:20:30Z

Juanas:

Quite often, a method used to solve a problem in probability can be used to solve many other problems which at first glance appear different, but are conceptually the same. This exercise illustrates this.

Go to the matching experiment in SOCR http://socr.stat.ucla.edu/htmls/SOCR_Experiments.html
Run it several times and play with it until you feel comfortable with it. Then use it and interpret it appropriately to answer the following problems:

(1) Four students are working on a project for their mathematics class that requires a lot of graphing and calculations. As they work, they pass around the calculators so that everyone can record their results. When the bell rings, each student grabs the nearest calculator and hurriedly leaves the room. What is the probability that none of the students too his or her calculator?
Attach a snapshot of the applet that shows how you found your answer with SOCR. (the snapshot should show the theoretical true probability and the probability you got by repeating this experiment 1000 times. Highlight what in the snapshot is your answer.

(2) 20 ladies arrive to a party and leave their coats with the concierge, who is not a very organized person. At the end of the party, the ladies don’t really remember what their coats look like (too much dancing and chocolate cake) and have lost the numbers the concierge give them. So the concierge has to give them the coats back at random. What is the probability that at least two ladies get their own coat?
Attach a snapshot of the applet that shows how you found your answer with SOCR. (the snapshot should show the theoretical true probability and the probability you got by repeating (appropriately) this experiment 1000 times. Highlight what in the snapshot is your answer.

SOCR EduMaterials Activities Matching Juana oct10-06 version1

2006-10-27T15:15:43Z

Juanas:

SOCR EduMaterials ExperimentsActivities

2006-10-27T15:12:10Z

Juanas: /* [http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials SOCR Educational Materials] - Experiments Activities */

== [http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials SOCR Educational Materials] - Experiments Activities ==

* [[SOCR_EduMaterials_Activities_DieCoin | SOCR Die Coin Experiment Activity]]
* [[SOCR_EduMaterials_Activities_CardsCoinsSampling | Cards & Coins Sampling Activity]]
* [[SOCR_EduMaterials_Activities_MontyHall | SOCR Monty Hall Experiment Activity]]
* [[SOCR_EduMaterials_Activities_DiceExperiment | SOCR Dice Experiment Activity]]
* [[SOCR_EduMaterials_Activities_CoinDieExperiment | SOCR Coin Die Experiment Activity]]
[[SOCR_EduMaterials_Activities_Matching_Juana_oct10-06_version1 | SOCR Matching calculators to owners]]

<hr>
* SOCR Home page: http://www.socr.ucla.edu

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SOCR EduMaterials Activities

2006-10-16T01:14:31Z

Juanas:

== [[SOCR_EduMaterials | SOCR Educational Materials]] - Activities ==

* [[SOCR_EduMaterials_Activities_Birthday | SOCR Birthday Experiment Activity ]]
* [[SOCR_EduMaterials_Activities_Bivariate | SOCR Bivariate Experiment Activity ]]
* [[SOCR_EduMaterials_Activities_CardsCoinsSampling | SOCR Cards and Coins Sampling Activity ]]
* [[SOCR_EduMaterials_Activities_CLT | SOCR Central Limit Theorem Activity ]]
* [[SOCR_EduMaterials_Activities_ConfidenceIntervals | SOCR Confidence Intervals Activity ]]
* [[SOCR_EduMaterials_Activities_Distributions | SOCR Distributions Activity ]]
* [[SOCR_EduMaterials_Activities_Triangles | SOCR Triangles Experiment Activity ]]
[[SOCR_EduMaterials_Activities_matching | SOCR Matching activity]]

* SOCR Template Activity : [[Image:SOCR_CLT_Activity_Key.doc ]]

* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities}}

SOCR EduMaterials Activities

2006-10-16T01:13:49Z

Juanas:

== [[SOCR_EduMaterials | SOCR Educational Materials]] - Activities ==

* [[SOCR_EduMaterials_Activities_Birthday | SOCR Birthday Experiment Activity ]]
* [[SOCR_EduMaterials_Activities_Bivariate | SOCR Bivariate Experiment Activity ]]
* [[SOCR_EduMaterials_Activities_CardsCoinsSampling | SOCR Cards and Coins Sampling Activity ]]
* [[SOCR_EduMaterials_Activities_CLT | SOCR Central Limit Theorem Activity ]]
* [[SOCR_EduMaterials_Activities_ConfidenceIntervals | SOCR Confidence Intervals Activity ]]
* [[SOCR_EduMaterials_Activities_Distributions | SOCR Distributions Activity ]]
* [[SOCR_EduMaterials_Activities_Triangles | SOCR Triangles Experiment Activity ]]
[[SOCR_EduMaterials_Activities_MyNewActivity | SOCR Matching activity]]

* SOCR Template Activity : [[Image:SOCR_CLT_Activity_Key.doc ]]

* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities}}

SOCR EduMaterials Activities Bivariate

2006-09-18T17:26:35Z

Juanas:

== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR Bivariate Activity ==

The Java applet needed for the following two activities can be found in the SOCR site

http://socr.stat.ucla.edu/htmls/SOCR_experiments.html

The Bivariate Normal Experiment ΔΘΖ

This experiment consists of selecting values for the random variables X and Y which are jointly normally distributed as a bivariate normal f(X,Y) with parameters x=0, y=0, x=”a value of your choice” , y=”a value of your choice” , and =”a value of your choice”. The first objective of our activity is to see how the location of the base of the distribution and its spread changes as the parameters change. The second objective is to see how no matter what the values of the parameters are, the marginal distribution of X and the marginal distribution of Y are both normal, with more or less spread depending on the values you assign to the parameters.

The points you select on the left hand side diagram, which shows the area above which the normal density lies (or area of integration), can be chosen by setting stop=10,000 update=100 and then clicking on the  button.

(A) See what happens when  and the standard deviation of Y are constant, and the standard deviations of X increases.

A.1 Start by setting =0.6, x=1.3 and y=1.1 and select the 10000 points as indicated above. Print a screen shot of the pictures you get. Attach at the end, well labeled so that we know it is for this question.
Write down the mean and standard deviation of the numbers you generated and the correlation.

A.2 Change now only the standard deviation of X from 1.3 to 2. Print a screen shot of the pictures. Write means, standard deviations and correlations of numbers you gnerated.

A.3 Compare the pictures in A.1 and A.2. What would you say has been the effect on the joint distribution f(X,Y) of increasing the standard deviation of X, other things held constant. Write your comments here.

A.4. Compare the marginal densities for X and for Y in A.1 and A.2. Which is more spread out?

A.5. Compare the regression lines in A.1 and A.2. Make your comparison in terms of the slope.

(B). See what happens when the standard deviations of X and Y are fixed and the correlation increases.

B.1 Fix now the standard deviation of X to 1.3 and the standard deviation of Y to 1.1 and the correlation coefficient to 0.9.
Print a screenshot of the pictures, means, standard deviations and correlations in your data. Compare your pictures to those in part A.1.

B.2. According to your results in part A.1, what has happened to the joint density function of X and Y as the correlation coefficient has increased?

What has happened to the regression line?

What has happened to the marginal densities of X and of Y?

C. Write here the joint density function of X and Y with parameter values as in A.1

Write the formula for the marginal density of X and the marginal density of Y with parameter values as given in A.1

Write the formulas for the conditional densities of X given Y and Y given X, with parameter values as given in A.1. Write then the regression lines that follow from these densities.

* SOCR Home page: http://www.socr.ucla.edu

\end{document}

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Bivariate}}

SOCR EduMaterials Activities Bivariate

2006-09-18T17:22:35Z

Juanas:

== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR Bivariate Activity ==

The Java applet needed for the following two activities can be found in the SOCR site

http://socr.stat.ucla.edu/htmls/SOCR_experiments.html

The Bivariate Normal Experiment

This experiment consists of selecting values for the random variables X and Y which are jointly normally distributed as a bivariate normal f(X,Y) with parameters x=0, y=0, x=”a value of your choice” , y=”a value of your choice” , and =”a value of your choice”. The first objective of our activity is to see how the location of the base of the distribution and its spread changes as the parameters change. The second objective is to see how no matter what the values of the parameters are, the marginal distribution of X and the marginal distribution of Y are both normal, with more or less spread depending on the values you assign to the parameters.

The points you select on the left hand side diagram, which shows the area above which the normal density lies (or area of integration), can be chosen by setting stop=10,000 update=100 and then clicking on the  button.

(A) See what happens when  and the standard deviation of Y are constant, and the standard deviations of X increases.

A.1 Start by setting =0.6, x=1.3 and y=1.1 and select the 10000 points as indicated above. Print a screen shot of the pictures you get. Attach at the end, well labeled so that we know it is for this question.
Write down the mean and standard deviation of the numbers you generated and the correlation.

A.2 Change now only the standard deviation of X from 1.3 to 2. Print a screen shot of the pictures. Write means, standard deviations and correlations of numbers you gnerated.

A.3 Compare the pictures in A.1 and A.2. What would you say has been the effect on the joint distribution f(X,Y) of increasing the standard deviation of X, other things held constant. Write your comments here.

A.4. Compare the marginal densities for X and for Y in A.1 and A.2. Which is more spread out?

A.5. Compare the regression lines in A.1 and A.2. Make your comparison in terms of the slope.

(B). See what happens when the standard deviations of X and Y are fixed and the correlation increases.

B.1 Fix now the standard deviation of X to 1.3 and the standard deviation of Y to 1.1 and the correlation coefficient to 0.9.
Print a screenshot of the pictures, means, standard deviations and correlations in your data. Compare your pictures to those in part A.1.

B.2. According to your results in part A.1, what has happened to the joint density function of X and Y as the correlation coefficient has increased?

What has happened to the regression line?

What has happened to the marginal densities of X and of Y?

C. Write here the joint density function of X and Y with parameter values as in A.1

Write the formula for the marginal density of X and the marginal density of Y with parameter values as given in A.1

Write the formulas for the conditional densities of X given Y and Y given X, with parameter values as given in A.1. Write then the regression lines that follow from these densities.

* SOCR Home page: http://www.socr.ucla.edu

\end{document}

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Bivariate}}

SOCR EduMaterials Activities Bivariate

2006-09-18T17:21:19Z

Juanas:

== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR Bivariate Activity ==
\documentclass[11pt]{article}
\usepackage{graphicx}
\usepackage{amssymb}

\textwidth = 6.5 in
\textheight = 9 in
\oddsidemargin = 0.0 in
\evensidemargin = 0.0 in
\topmargin = 0.0 in
\headheight = 0.0 in
\headsep = 0.0 in
\parskip = 0.2in
\parindent = 0.0in

\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{definition}{Definition}

\title{Brief Article}
\author{The Author}
\begin{document}
\maketitle

The Java applet needed for the following two activities can be found in the SOCR site

http://socr.stat.ucla.edu/htmls/SOCR_experiments.html

The Bivariate Normal Experiment

The quadratic formula is $$-b \pm \sqrt{b^2 - 4ac} \over 2a$$
\bye

This experiment consists of selecting values for the random variables X and Y which are jointly normally distributed as a bivariate normal f(X,Y) with parameters x=0, y=0, x=”a value of your choice” , y=”a value of your choice” , and =”a value of your choice”. The first objective of our activity is to see how the location of the base of the distribution and its spread changes as the parameters change. The second objective is to see how no matter what the values of the parameters are, the marginal distribution of X and the marginal distribution of Y are both normal, with more or less spread depending on the values you assign to the parameters.

The points you select on the left hand side diagram, which shows the area above which the normal density lies (or area of integration), can be chosen by setting stop=10,000 update=100 and then clicking on the  button.

(A) See what happens when  and the standard deviation of Y are constant, and the standard deviations of X increases.

A.1 Start by setting =0.6, x=1.3 and y=1.1 and select the 10000 points as indicated above. Print a screen shot of the pictures you get. Attach at the end, well labeled so that we know it is for this question.
Write down the mean and standard deviation of the numbers you generated and the correlation.

A.2 Change now only the standard deviation of X from 1.3 to 2. Print a screen shot of the pictures. Write means, standard deviations and correlations of numbers you gnerated.

A.3 Compare the pictures in A.1 and A.2. What would you say has been the effect on the joint distribution f(X,Y) of increasing the standard deviation of X, other things held constant. Write your comments here.

A.4. Compare the marginal densities for X and for Y in A.1 and A.2. Which is more spread out?

A.5. Compare the regression lines in A.1 and A.2. Make your comparison in terms of the slope.

(B). See what happens when the standard deviations of X and Y are fixed and the correlation increases.

B.1 Fix now the standard deviation of X to 1.3 and the standard deviation of Y to 1.1 and the correlation coefficient to 0.9.
Print a screenshot of the pictures, means, standard deviations and correlations in your data. Compare your pictures to those in part A.1.

B.2. According to your results in part A.1, what has happened to the joint density function of X and Y as the correlation coefficient has increased?

What has happened to the regression line?

What has happened to the marginal densities of X and of Y?

C. Write here the joint density function of X and Y with parameter values as in A.1

Write the formula for the marginal density of X and the marginal density of Y with parameter values as given in A.1

Write the formulas for the conditional densities of X given Y and Y given X, with parameter values as given in A.1. Write then the regression lines that follow from these densities.

* SOCR Home page: http://www.socr.ucla.edu

\end{document}

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Bivariate}}

SOCR EduMaterials Activities Bivariate

2006-09-18T17:18:54Z

Juanas:

== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR Bivariate Activity ==

The Java applet needed for the following two activities can be found in the SOCR site

http://socr.stat.ucla.edu/htmls/SOCR_experiments.html

The Bivariate Normal Experiment

The quadratic formula is $$-b \pm \sqrt{b^2 - 4ac} \over 2a$$
\bye

This experiment consists of selecting values for the random variables X and Y which are jointly normally distributed as a bivariate normal f(X,Y) with parameters x=0, y=0, x=”a value of your choice” , y=”a value of your choice” , and =”a value of your choice”. The first objective of our activity is to see how the location of the base of the distribution and its spread changes as the parameters change. The second objective is to see how no matter what the values of the parameters are, the marginal distribution of X and the marginal distribution of Y are both normal, with more or less spread depending on the values you assign to the parameters.

The points you select on the left hand side diagram, which shows the area above which the normal density lies (or area of integration), can be chosen by setting stop=10,000 update=100 and then clicking on the  button.

(A) See what happens when  and the standard deviation of Y are constant, and the standard deviations of X increases.

A.1 Start by setting =0.6, x=1.3 and y=1.1 and select the 10000 points as indicated above. Print a screen shot of the pictures you get. Attach at the end, well labeled so that we know it is for this question.
Write down the mean and standard deviation of the numbers you generated and the correlation.

A.2 Change now only the standard deviation of X from 1.3 to 2. Print a screen shot of the pictures. Write means, standard deviations and correlations of numbers you gnerated.

A.3 Compare the pictures in A.1 and A.2. What would you say has been the effect on the joint distribution f(X,Y) of increasing the standard deviation of X, other things held constant. Write your comments here.

A.4. Compare the marginal densities for X and for Y in A.1 and A.2. Which is more spread out?

A.5. Compare the regression lines in A.1 and A.2. Make your comparison in terms of the slope.

(B). See what happens when the standard deviations of X and Y are fixed and the correlation increases.

B.1 Fix now the standard deviation of X to 1.3 and the standard deviation of Y to 1.1 and the correlation coefficient to 0.9.
Print a screenshot of the pictures, means, standard deviations and correlations in your data. Compare your pictures to those in part A.1.

B.2. According to your results in part A.1, what has happened to the joint density function of X and Y as the correlation coefficient has increased?

What has happened to the regression line?

What has happened to the marginal densities of X and of Y?

C. Write here the joint density function of X and Y with parameter values as in A.1

Write the formula for the marginal density of X and the marginal density of Y with parameter values as given in A.1

Write the formulas for the conditional densities of X given Y and Y given X, with parameter values as given in A.1. Write then the regression lines that follow from these densities.

* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Bivariate}}

SOCR EduMaterials Activities Bivariate

2006-09-18T17:16:19Z

Juanas:

== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR Bivariate Activity ==

The Java applet needed for the following two activities can be found in the SOCR site

http://socr.stat.ucla.edu/htmls/SOCR_experiments.html

The Bivariate Normal Experiment -NEW!!

This experiment consists of selecting values for the random variables X and Y which are jointly normally distributed as a bivariate normal f(X,Y) with parameters x=0, y=0, x=”a value of your choice” , y=”a value of your choice” , and =”a value of your choice”. The first objective of our activity is to see how the location of the base of the distribution and its spread changes as the parameters change. The second objective is to see how no matter what the values of the parameters are, the marginal distribution of X and the marginal distribution of Y are both normal, with more or less spread depending on the values you assign to the parameters.

The points you select on the left hand side diagram, which shows the area above which the normal density lies (or area of integration), can be chosen by setting stop=10,000 update=100 and then clicking on the  button.

(A) See what happens when  and the standard deviation of Y are constant, and the standard deviations of X increases.

A.1 Start by setting =0.6, x=1.3 and y=1.1 and select the 10000 points as indicated above. Print a screen shot of the pictures you get. Attach at the end, well labeled so that we know it is for this question.
Write down the mean and standard deviation of the numbers you generated and the correlation.

A.2 Change now only the standard deviation of X from 1.3 to 2. Print a screen shot of the pictures. Write means, standard deviations and correlations of numbers you gnerated.

A.3 Compare the pictures in A.1 and A.2. What would you say has been the effect on the joint distribution f(X,Y) of increasing the standard deviation of X, other things held constant. Write your comments here.

A.4. Compare the marginal densities for X and for Y in A.1 and A.2. Which is more spread out?

A.5. Compare the regression lines in A.1 and A.2. Make your comparison in terms of the slope.

(B). See what happens when the standard deviations of X and Y are fixed and the correlation increases.

B.1 Fix now the standard deviation of X to 1.3 and the standard deviation of Y to 1.1 and the correlation coefficient to 0.9.
Print a screenshot of the pictures, means, standard deviations and correlations in your data. Compare your pictures to those in part A.1.

B.2. According to your results in part A.1, what has happened to the joint density function of X and Y as the correlation coefficient has increased?

What has happened to the regression line?

What has happened to the marginal densities of X and of Y?

C. Write here the joint density function of X and Y with parameter values as in A.1

Write the formula for the marginal density of X and the marginal density of Y with parameter values as given in A.1

Write the formulas for the conditional densities of X given Y and Y given X, with parameter values as given in A.1. Write then the regression lines that follow from these densities.

* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Bivariate}}