SOCR EduMaterials Activities Bivariate
cheap xanax online lorazepam free real ringtones punk ringtones buy albuterol cheap xanax online fioricet didrex online verizon ringtones ultracet online tracfone ringtones cheap clomid online ativan buy xanax buy nexium free sonyericsson ringtones cheap clomid cheap adipex online cialis hydrocodone online cheap levitra free midi ringtones cheap lisinopril free wwe ringtones phentermine online tracfone ringtones cheap sildenafil free verizon ringtones midi ringtones phentermine online cheap rivotril vicodin online celexa online funny ringtones flexeril online hoodia online tenuate online prozac online sprint ringtones norco online meridia online free sprint ringtones diazepam online fioricet free mp3 ringtones paxil online buy zanaflex but alprazolam soma online order diazepam wwe ringtones but zoloft buy lorazepam online norco free ringtones carisoprodol online free qwest ringtones cheap clonazepam cheap celexa clonazepam online lipitor online nokia ringtones cheap lisinopril cheap propecia free nokia ringtones free punk ringtones carisoprodol online cheap ultram sony ericsson ringtones free tracfone ringtones cheap zyban cheap hoodia cheap tramadol cingular ringtones free jazz ringtones free alltel ringtones cheap flexeril free nextel ringtones kyocera ringtones samsung ringtones free motorola ringtones meridia online cheap xenical free sony ringtones paxil online free sagem ringtones ativan online cheap rivotril order ortho celexa online sharp ringtones adipex online cheap ortho cheap hydrocodone propecia online cingular ringtones nextel ringtones free sagem ringtones adipex free punk ringtones didrex online sonyericsson ringtones didrex online diazepam online free samsung ringtones sharp ringtones order meridia mono ringtones valium online buy hgh nextel ringtones free funny ringtones cheap lortab ultracet viagra online online albuterol vicodin online motorola ringtones lorazepam online ericsson ringtones free mp3 ringtones free sonyericsson ringtones viagra online cheap cyclobenzaprine vigrx free wwe ringtones cheap zoloft clomid online cheap fioricet free samsung ringtones albuterol online tramadol online xenical online alprazolam online cheap clonazepam free mp3 ringtones norco online xanax mtv ringtones qwest ringtones valium online cheap sildenafil zyban online alprazolam online online levitra soma online cheap ortho cheap xenical cheap zyban free polyphonic ringtones motorola ringtones lisinopril online sagem ringtones music ringtones cheap ativan jazz ringtones cool ringtones ericsson ringtones tracfone ringtones but norco viagra online sony ericsson ringtones nexium online paxil online free cool ringtones vicodin online kyocera ringtones jazz ringtones free sprint ringtones cheap cialis cyclobenzaprine online free nokia ringtones paxil online cheap lipitor buy cyclobenzaprine prozac online ultram online cheap pharmacy online cheap rivotril free sony ringtones buy fioricet cheap tenuate cheap viagra real ringtones zanaflex online midi ringtones cheap ativan buy clonazepam diethylpropion online verizon ringtones free free ringtones free online pharmacy soma online free ringtones vigrx cheap lortab free sony ringtones buy wellbutrin hgh online free kyocera ringtones == SOCR Educational Materials - Activities - SOCR Bivariate Activity ==
The Bivariate Normal Experiment: 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
- Setting: 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 \(\mu_x=0\), \(\mu_y=0\), \(\sigma_x\)=”a value of your choice” , \(\sigma_y\)=”a value of your choice” , and \(\rho\)=”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 <RUN> button.
See what happens when \(\rho\) and the standard deviation of Y, \(\sigma_y\), are constant, and the standard deviations of X, \(\sigma_x\), increases
- Exercise 1: Next, set \(\rho=0.6, \sigma_x=1.3\) and \(\sigma_y=1.1\) and select the 10,000 points as indicated above. Write down the mean and standard deviation of the numbers you generated and the correlation. Save the picture.
- Exercise 2: Now, change only the standard deviation of X from 1.3 to 2. Write down the means, standard deviations and correlations of numbers you gnerated. Save the picture.
- Exercise 3: Compare the pictures generated in Exercise 1 and 2 above. What would you say is the effect on the joint distribution \(f(X,Y)\) of increasing the standard deviation of X, other things held constant. Write your comments here.
- Exercise 4: Compare the marginal densities for X and for Y in Exercise 1 and 2. Which density is more spread out?
- Exercise 5: Compare the regression lines in Exercise 1 and 2. Make your comparison in terms of the slope.
See what happens when the standard deviations of X and Y are fixed and the correlation increases
- Exercise 6: 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 Exercise 1.
- Exercise 7: According to your results in execrsize 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?
Write here the joint density function of X and Y with parameter values as in Exercise 1
- Exercise 8: Write the formula for the marginal density of X and the marginal density of Y with parameter values as given in Exercise 1. Write the formulas for the conditional densities of X given Y and Y given X, with parameter values as given in Exercise 1. Write then the regression lines that follow from these densities.
- SOCR Home page: http://www.socr.ucla.edu
Translate this page:
