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