# SOCR EduMaterials Activities ExpDist

## Contents

## This is an activity to explore the Exponential Distribution: Learn how to compute probabilities, densities, and percentiles

**Description**

You can access the applet for the Exponential Distributions

- Graph and print
- \(X \sim exp(0.2)\)
- \(X \sim exp(1)\)
- \(X \sim exp(10)\)

- \(X \sim exp(0.2)\)

- 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.

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

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