Question: 12. A continuous random variable $X$ has probability density function $$ begin{aligned} f(x) &=frac{1}{2 sqrt{x}} quad 1 leq x leq 4 &=0 quad text

12. A continuous random variable $X$ has probability density function $$

12. A continuous random variable $X$ has probability density function $$ \begin{aligned} f(x) &=\frac{1}{2 \sqrt{x}} \quad 1 \leq x \leq 4 \\ &=0 \quad \text { otherwise. } \end{aligned) $$ What is the expected value of $X ?$ (to three decimals) A. $2.485$ B. $2.365$ C. $1.555$ D. $2.333$ E. None of the above. 13. For $X$ in the previous problem, find $\operatorname{Pr}(X>3)$. (to three decimals) A. 268 B. 317 C. .727 D. .538 E. None of the above. SP.JG.095

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