# SOCR EduMaterials Activities ExpDist

### From Socr

## 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

- 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:

- Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:

- Graph and print

- 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

## **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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