Monthly Archives: December, 2018

Exam P Practice Problem 104 – two random insurance losses

Problem 104-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 is exactly 2, what is the probability that Y is less than 1?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \frac{7}{24}

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \frac{11}{24}

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \frac{12}{24}

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \frac{13}{24}

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \frac{14}{24}

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Problem 104-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. Determine the probability that Y exceeds 2 given that the loss X is known to be 2.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \frac{13}{36}

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \frac{24}{36}

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \frac{26}{36}

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \frac{28}{36}

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \frac{29}{36}

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Answers

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