Exam P Practice Problem 86 – Finding Mean and Variance

The following is the cumulative distribution function of the random variable X.

    \displaystyle F(x)=\left\{\begin{matrix} \displaystyle 0&\ \ \ \ \ \ x < 0 \\{\text{ }}& \\{\displaystyle \frac{(x+2)^2}{100}}&\ \ \ \ \ \ 0 \le x <6 \\{\text{ }}& \\{\displaystyle 1}&\ \ \ \ \ \ 6 \le x <\infty  \end{matrix}\right.

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Problem 86-A

Calculate the expected value of X.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   2.16

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   3.35

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   4.32

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   6.00

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   6.67

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Problem 86-B

Calculate the variance of X.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 3.240

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 3.658

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 3.957

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 4.694

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 5.556

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Answers

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

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