SOCR EduMaterials Activities ExpDist
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
- \(X \sim exp(0.2)\)
- \(X \sim exp(1)\)
- \(X \sim exp(10)\)
- \(X \sim exp(0.2)\)
- 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\[\[ x_p=\frac{ln(1-\frac{p}{100})}{-\lambda}\]\]
- Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula\[\[ P(X \le x)=1-e^{-\lambda x} \]\]
- Graph and print
- \(X \sim N(2,0.5)\)
- \(X \sim N(10,2)\)
- \(X \sim N(20,5)\)
- 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
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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.
- SOCR Home page: http://www.socr.ucla.edu
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