Exam P Practice Problem 89 – Finding Median

Problem 89-A

The random variables X and Y have the following joint density function.

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

Suppose that m is the median of X+Y. Which of the following is true about m?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   2.5<m<3

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   2<m<3

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   3<m<4

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   3.5<m<4

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   3.5<m<4.5

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Problem 89-B

The random variable X has the following density function.

    \displaystyle f(x)=\frac{3}{16000} \ (400-x^2) \ \ \ \ \ \ \ 0<x<20

Suppose that m is the median of X. Which of the following is true about m?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   6<m<7

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   5.5<m<6

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   5.5<m<6.5

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   7<m<8

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   7<m<9

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Answers

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\copyright \ 2014 \ \ \text{ Dan Ma}

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3 responses

  1. I need to see the solution for 89-A

  2. Nicholas Ouellet | Reply

    89-A is wrong. The cum. distribution for S=X+Y for S less than 4 is (1/16)s^2-(1/192)s^3 and this part of the distribution holds 2/3 of the density by plugging in 4. Trying some numbers says the median is around 3.33. Answer C is correct. Not A.

    1. You are right. C is the answer for 89-A. Thanks for pointing it out.

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