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Suppose that a random variable Y has a probability density
Chapter 4, Problem 96E(choose chapter or problem)
Suppose that a random variable \(Y\) has a probability density function given by
\(f(y)=\left\{\begin{array}{ll} k y^{3} e^{-y / 2}, & y>0, \\ 0, & \text { elsewhere. } \end{array}\right.\)
a. Find the value of \(k\) that makes \(f(y)\) a density function.
b. Does \(Y\) have a \(x^{2}\) distribution? If so, how many degrees of freedom?
c. What are the mean and standard deviation of \(Y\)?
d. Applet Exercise. What is the probability that \(Y\) lies within 2 standard deviations of its mean?
Questions & Answers
(2 Reviews)
QUESTION:
Suppose that a random variable \(Y\) has a probability density function given by
\(f(y)=\left\{\begin{array}{ll} k y^{3} e^{-y / 2}, & y>0, \\ 0, & \text { elsewhere. } \end{array}\right.\)
a. Find the value of \(k\) that makes \(f(y)\) a density function.
b. Does \(Y\) have a \(x^{2}\) distribution? If so, how many degrees of freedom?
c. What are the mean and standard deviation of \(Y\)?
d. Applet Exercise. What is the probability that \(Y\) lies within 2 standard deviations of its mean?
ANSWER:Step1 of 4
Goals:
a. Find the value of k that makes \(f(y)=k y^{3} e^{-y / 2}\) for \(y>0\), a density function.
b. Does \(Y\) have a \(x^{2}\) distribution? If so, how many degrees of freedom?
c. What is the mean and standard deviation of \(Y\) ?
d. Applet Exercise What is the probability that \(Y\) lies within 2 standard deviations
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Review this written solution for 31764) viewed: 263 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 4 - Problem 96e
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