The relative humidity Y, when measured at a location, has a probability density function given by [ky³(1−y)², 0≤y ≤ 1, elsewhere. f(y) = 0, a Find the value of k that makes f(y) a density function.
The relative humidity Y, when measured at a location, has a probability density function given by [ky³(1−y)², 0≤y ≤ 1, elsewhere. f(y) = 0, a Find the value of k that makes f(y) a density function.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![The relative humidity \( Y \), when measured at a location, has a probability density function given by
\[
f(y) =
\begin{cases}
ky^3(1-y)^2, & 0 \leq y \leq 1, \\
0, & \text{elsewhere}.
\end{cases}
\]
**a** Find the value of \( k \) that makes \( f(y) \) a density function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6389447-1237-4af0-b5c6-eb1260425b55%2F392e347b-0cbb-475e-ae58-d71803be7ed7%2Fe35dbhe_processed.png&w=3840&q=75)
Transcribed Image Text:The relative humidity \( Y \), when measured at a location, has a probability density function given by
\[
f(y) =
\begin{cases}
ky^3(1-y)^2, & 0 \leq y \leq 1, \\
0, & \text{elsewhere}.
\end{cases}
\]
**a** Find the value of \( k \) that makes \( f(y) \) a density function.
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