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The proportion of time per day that all checkout counters
Chapter 4, Problem 28E(choose chapter or problem)
The proportion of time per day that all checkout counters in a supermarket are busy is a random variable with density function
\(f(y)=\left\{\begin{array}{ll}
c y^{2}(1-y)^{4}, & 0 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the value of that makes \(f(y)\) a probability density function.
b Find \(E(Y)\).
Equation Transcription:
Text Transcription:
Questions & Answers
QUESTION:
The proportion of time per day that all checkout counters in a supermarket are busy is a random variable with density function
\(f(y)=\left\{\begin{array}{ll}
c y^{2}(1-y)^{4}, & 0 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the value of that makes \(f(y)\) a probability density function.
b Find \(E(Y)\).
Equation Transcription:
Text Transcription:
ANSWER:
Solution:
Step 1 of 2:
Let Y be a random variable with the density function
- The claim is to find the value of c that makes f(y) a probability density function
Let, dy
= c dy
Then, c =
= 105
Hence, c = 105