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

  • Graph and print
    • X \sim exp(0.2)
    • X \sim exp(1)
    • X \sim exp(10)
  • 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

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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