Exam P Practice Problem 59 – Joint Distributions

Problem 59-A

Two random losses X and Y are jointly modeled by the following density function:

      \displaystyle f(x,y)=\frac{1}{32} \ (4-x) \ (4-y) \ \ \ \ \ \ 0<x<4, \ 0<y<x

Suppose that both of these losses had occurred. Given that X exceeds 2, what is the probability that Y is less than 2?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.4000

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.4667

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.7518

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.8571

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.9375

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Problem 59-B

Two random losses X and Y are jointly modeled by the following density function:

      \displaystyle f(x,y)=\frac{1}{96} \ (x+2y) \ \ \ \ \ \ 0<x<4, \ 0<y<4

Suppose that both of these losses had occurred. What is the probability that only one of them exceeds 2?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.1250

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.2083

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.2917

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.3750

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.5000

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Answers

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\copyright \ 2013

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