# SOCR EduMaterials Activities Exponential Distribution

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

\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

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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.