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Let A and B two random events and P(A)-1/2, P(B)-1/5. and P(A | B)- 1/4. Assume X-B(1, P(A)) and Y-B(1, P(B)). Find (1) The joint mass function of X and Y. (2) E(min (X, Y))

Let A and B two random events and P(A)-1/2, P(B)-1/5. and P(A | B)- 1/4. Assume X-B(1, P(A)) and Y-B(1, P(B)). Find (1) The joint mass function of X and Y. (2) E(min (X, Y))

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let A and B two random events and P(A)=1/2, P(B)=1/5, and P(A | B)= 1/4. Assume X-B(1, P(A)) and Y-B(1, P(B)). Find (1) The joint mass function of X and Y. (2) E(min(X, Y})
Transcribed Image Text:Let A and B two random events and P(A)=1/2, P(B)=1/5, and P(A | B)= 1/4. Assume X-B(1, P(A)) and Y-B(1, P(B)). Find (1) The joint mass function of X and Y. (2) E(min(X, Y})
Expert Solution
Step 1: Determine the given variable

Let A and B be two random events and:    

P left parenthesis A right parenthesis equals 1 half P left parenthesis B right parenthesis equals 1 fifth P left parenthesis A ∣ B right parenthesis equals 1 fourth

Assume:

X tilde B left parenthesis 1 comma P left parenthesis A right parenthesis right parenthesis Y tilde B left parenthesis 1 comma P left parenthesis B right parenthesis right parenthesis

Where B(1, p) denotes a Bernoulli distribution with a success probability p.

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