Let X denote the amount of time a book on two-hour reserve is actually checked out

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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.

\(F(x)= \begin{cases}0 & x<0 \\ \frac{x^{2}}{25} & 0 \leq x<5 \\ 1 & 5 \leq x\end{cases}\)

Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)

(a) Calculate P(X ≤ 2)

(b) Calculate P(1.5 ≤ x ≤ 2).

(c) Calculate P(X>2.5).

(d) What is the median checkout duration \tilde{μ} ? [solve 0.5=F(\tilde{μ})].

(e) Obtain the density function f(x).

f(x)=F'(x)=

(f) Calculate E(X).

(g) Calculate V(X) and σx.

V(X)=

σx=

(h) If the borrower is charged an amount h(X)=X² when checkout duration is X, compute the expected charge E[h(X)]

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 2 2

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Let X denote the amount of time a book on two-hour reserve is actually checked out

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