GW 2.13

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Florida International University *

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2122

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Statistics

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Feb 20, 2024

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docx

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Uploaded by MasterDiscovery11757

Lab Module 4: Discrete Random Variables Question 1: Define the following discrete random variables: X: The number of heads appearing in a three coin toss. Y: The number of queens appearing in a set of three cards drawn without replacement from a standard 52-card deck. a) Sketch the PDF of X and the PDF of Y. X=0: 0.125/ X=1: 0.375/ X=2: 0.375/ X=3: 0.125 Y=0: 0.783/ Y=1: 0.204/ Y=2: 0.013/ Y=3: 0.0002 b) Sketch the CDF of X and the CDF of Y. Compare P(X ≤ 1) and P(Y ≤ 1). X= 0.5 , Y= 0.984 c) The random variables X and Y share a common domain (0,1,2,3). How do their probability distributions appear different? d) Compute E(X) and E(Y). Does X or Y have the larger expected value? Is this re- sult expected based on the PDFs of X and Y? e) Compute Var(X) and Var(Y). Does X or Y have the larger variance? Is this result expected based on the PDFs of X and Y? Question 2: Define the discrete random variable R: the total number of rainy days in a week in Miami, Florida. The PDF of R is depicted below: Lab Module 4 - Worksheet a) Sketch the CDF of R. What proportion of weeks have less than or equal to three days of rain? b) Compute E(R), the expected number of days of rain per week.

c) Compute Var(R). How does Var(R) compare to the variance of a uniform random variable with the same domain as R?

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GW 2.13

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