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) = 0 16 1 x < 0 0 3.5). 4≤X Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). (b) Calculate P(2.5 ≤ x ≤ 3).
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) = 0 16 1 x < 0 0 3.5). 4≤X Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). (b) Calculate P(2.5 ≤ x ≤ 3).
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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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.
\[
F(x) =
\begin{cases}
0 & x < 0 \\
\frac{x^2}{16} & 0 \leq x < 4 \\
1 & 4 \leq x
\end{cases}
\]
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate \( P(X \leq 3) \).
\[ \text{Answer:} \]
(b) Calculate \( P(2.5 \leq X \leq 3) \).
\[ \text{Answer:} \]
(c) Calculate \( P(X > 3.5) \).
\[ \text{Answer:} \]
(d) What is the median checkout duration \( \tilde{\mu} \)? [solve \( 0.5 = F(\tilde{\mu}) \)].
\[ \text{Answer:} \]
(e) Obtain the density function \( f(x) \).
\[
f(x) = F'(x)
\]
\[
=
\begin{cases}
\text{________} & 0 \leq x < 4 \\
0 & \text{otherwise}
\end{cases}
\]
(f) Calculate \( E(X) \).
\[ \text{Answer:} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F324f16c4-c4e5-4b06-b074-f261b39e021a%2F11952c91-273c-460a-9a43-d8d185e4f7aa%2F9ryv1z_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( X \) denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
\[
F(x) =
\begin{cases}
0 & x < 0 \\
\frac{x^2}{16} & 0 \leq x < 4 \\
1 & 4 \leq x
\end{cases}
\]
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate \( P(X \leq 3) \).
\[ \text{Answer:} \]
(b) Calculate \( P(2.5 \leq X \leq 3) \).
\[ \text{Answer:} \]
(c) Calculate \( P(X > 3.5) \).
\[ \text{Answer:} \]
(d) What is the median checkout duration \( \tilde{\mu} \)? [solve \( 0.5 = F(\tilde{\mu}) \)].
\[ \text{Answer:} \]
(e) Obtain the density function \( f(x) \).
\[
f(x) = F'(x)
\]
\[
=
\begin{cases}
\text{________} & 0 \leq x < 4 \\
0 & \text{otherwise}
\end{cases}
\]
(f) Calculate \( E(X) \).
\[ \text{Answer:} \]
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