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Solved: The proportion of time per day that all checkout
Chapter 4, Problem 133E(choose chapter or problem)
The proportion of time per day that all checkout counters in a supermarket are busy is a random variable with a density function given by
\(f(y)=\left\{\begin{array}{ll}
c y^{2}(1-y)^{4}, & 0 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the value of that makes \(f(y)\) a probability density function.
b Find \(E(Y)\). (Use what you have learned about the beta-type distribution. Compare your answers to those obtained in Exercise .)
c Calculate the standard deviation of .
d Applet Exercise Use the applet Beta Probabilities and Quantiles to find \(P(Y>\mu+2 \sigma)\).
Equation Transcription:
Text Transcription:
f(y)=
cy^2(1-y)^4, 0</=y</=1,
0, elsewhere.
f(y)
E(Y)
P(Y>mu+2sigma)
Questions & Answers
QUESTION:
The proportion of time per day that all checkout counters in a supermarket are busy is a random variable with a density function given by
\(f(y)=\left\{\begin{array}{ll}
c y^{2}(1-y)^{4}, & 0 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
a Find the value of that makes \(f(y)\) a probability density function.
b Find \(E(Y)\). (Use what you have learned about the beta-type distribution. Compare your answers to those obtained in Exercise .)
c Calculate the standard deviation of .
d Applet Exercise Use the applet Beta Probabilities and Quantiles to find \(P(Y>\mu+2 \sigma)\).
Equation Transcription:
Text Transcription:
f(y)=
cy^2(1-y)^4, 0</=y</=1,
0, elsewhere.
f(y)
E(Y)
P(Y>mu+2sigma)
ANSWER:
Solution:
Step 1 of 3:
The proportion of time per day that all checkout counters in a supermarket are busy is a random variable Y with a density function given by
We have to find
- The value of c that makes f(y) a probability density function.
- The mean, E(Y).
- The standard deviation of Y.
-
The probability P(Y>
by using applet.