# SOCR EduMaterials Activities ExpDist

## Description

You can access the applet for the Exponential Distributions

• Graph and print
• $$X \sim exp(0.2)$$
• $$X \sim exp(1)$$
• $$X \sim exp(10)$$
• Locate the maximum density for each one of these distributions.
• Find the height of the density at 3 values of $$X$$ (one near 0, one near the mean, and one towards the tail of the distribution).
• Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class$x_p=\frac{ln(1-\frac{p}{100})}{-\lambda}$
• Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula$P(X \le x)=1-e^{-\lambda x}$
• Graph and print
• $$X \sim N(2,0.5)$$
• $$X \sim N(10,2)$$
• $$X \sim N(20,5)$$
• Find one percentile for each one of these distributions and locate them on the printouts.
• Find one cumulative probability for each one of these distributions and locate them on the printouts.

## Exercise 1

Construct the joint probability distribution of X and Y.

## Exercise 2

Find the conditional expected value of Y given X=5.

## Exercise 3

Find the conditional variance of Y given X=5.

## Exercise 4

Find the expected value of Y.

## Exercise 5

Find the standard deviation of Y.

## Exercise 6

Graph the probability distribution of Y.

## Exercise 7

Use SOCR Experiments and choose "Die Coin Experiment" to graph and print the empirical distribution of Y when the experiment is performed:

• n = 1000 times.
• n= 10000 times
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## Exercise 8

Compare the theoretical mean and standard deviation of Y (exercise 4 and 5) with the empirical mean and standard deviation found in exercise 7.