# 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

\begin{itemize}
\item[a.] Graph and print \\
$X \sim exp(0.2)$ \\
$X \sim exp(1)$ \\
$X \sim exp(10)$
\begin{itemize}
\item[1.] Locate the maximum density for each one of these distributions.
\item[2.] 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).
\item[3.] Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class:
'"`UNIQ-MathJax1-QINU`"'
\item[4.] Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:
'"`UNIQ-MathJax2-QINU`"'
\end{itemize}
\item[b.] Graph and print \\
$X \sim N(2,0.5)$ \\
$X \sim N(10,2)$ \\
$X \sim N(20,5$
\begin{itemize}
\item[1.] Find one percentile for each one of these distributions and locate them on the printouts.
\item[2.] Find one cumulative probability for each one of these distributions and locate them on the printouts.
\end{itemize}

**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:

a. n = 1000 times.

b. 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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