SOCR EduMaterials Activities ExpDist
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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
Failed to parse (unknown function\begin): \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: \[ x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} \] \item[4.] Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula: \[ P(X \le x)=1-e^{-\lambda x} \] \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.
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