# SOCR EduMaterials Activities Exponential Distribution

## 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

- Here is the shape of the exponential distribution (this is a snpashot from the SOCR website:

**Exercise 1:**Graph and print:

a. exp(0.2) b. exp(1) c. exp(10)

**Exercise 2:**Locate the maximum density for each one of these distributions.

**Exercise 3:**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).

**Exercise 4:**Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class:

\[ x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} \]

**Exercise 5:**Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:

\[ P(X \le x)=1-e^{-\lambda x} \]

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

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