(a) Compute the cdf of X. x< 1 F(x) = 1SXS2 2 > x (b) Obtain an expression for the (100p)th percentile. nip) - What is the value of ? (Round your answer to three decimal places.) (c) Compute E(X) and V(X). (Round your answers to four decimal places.) thousand gallons thousand gallons squared E(X) - VX) = (d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week? [Hint: Let h(x) - amount left when demand - x.] (Round your answer to three decimal places.) thousand gallons
(a) Compute the cdf of X. x< 1 F(x) = 1SXS2 2 > x (b) Obtain an expression for the (100p)th percentile. nip) - What is the value of ? (Round your answer to three decimal places.) (c) Compute E(X) and V(X). (Round your answers to four decimal places.) thousand gallons thousand gallons squared E(X) - VX) = (d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week? [Hint: Let h(x) - amount left when demand - x.] (Round your answer to three decimal places.) thousand gallons
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![The weekly demand for propane gas (in thousands of gallons) from a particular facility is a random variable \(X\) with the following probability density function (pdf):
\[ f(x) =
\begin{cases}
2\left(1 - \dfrac{1}{x^2}\right) & 1 \leq x \leq 2 \\
0 & \text{otherwise}
\end{cases}
\]
(a) Compute the cumulative distribution function (cdf) of \(X\).
\[ F(x) =
\begin{cases}
0 & x < 1 \\
\text{[blank space]} & 1 \leq x \leq 2 \\
1 & 2 < x
\end{cases}
\]
(b) Obtain an expression for the \((100p)^{th}\) percentile.
\(\eta(p) = \text{[blank space]}\)
What is the value of \(\eta?\) (Round your answer to three decimal places.)
(c) Compute \(E(X)\) and \(V(X)\). (Round your answers to four decimal places.)
\(E(X) = \text{[blank space]}\) thousand gallons
\(V(X) = \text{[blank space]}\) thousand gallons squared
(d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week?
\( \text{Hint: Let } H(x) = \text{ amount left when demand } = x.\) (Round your answer to three decimal places.)
\(\text{[blank space]}\) thousand gallons](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4fac401-f688-4a8e-b637-a2500ce6ac46%2F2abd314f-362e-4a62-b0f4-f9a1fde98aac%2Foh6q13_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The weekly demand for propane gas (in thousands of gallons) from a particular facility is a random variable \(X\) with the following probability density function (pdf):
\[ f(x) =
\begin{cases}
2\left(1 - \dfrac{1}{x^2}\right) & 1 \leq x \leq 2 \\
0 & \text{otherwise}
\end{cases}
\]
(a) Compute the cumulative distribution function (cdf) of \(X\).
\[ F(x) =
\begin{cases}
0 & x < 1 \\
\text{[blank space]} & 1 \leq x \leq 2 \\
1 & 2 < x
\end{cases}
\]
(b) Obtain an expression for the \((100p)^{th}\) percentile.
\(\eta(p) = \text{[blank space]}\)
What is the value of \(\eta?\) (Round your answer to three decimal places.)
(c) Compute \(E(X)\) and \(V(X)\). (Round your answers to four decimal places.)
\(E(X) = \text{[blank space]}\) thousand gallons
\(V(X) = \text{[blank space]}\) thousand gallons squared
(d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week?
\( \text{Hint: Let } H(x) = \text{ amount left when demand } = x.\) (Round your answer to three decimal places.)
\(\text{[blank space]}\) thousand gallons
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