Solution Found!
The random variable Y, with a density function given by is
Chapter 4, Problem 186SE(choose chapter or problem)
The random variable 𝑌, with a density function given by
\(f(y)=\frac{m y^{m-1}}{\alpha} e^{-y^{m} / \alpha}, \quad 0 \leq y<\infty, \alpha, m>0\)
is said to have a Weibull distribution. The Weibull density function provides a good model
for the distribution of length of life for many mechanical devices and biological plants and
animals. Find the mean and variance for a Weibull distributed random variable with \(m=2\).
Equation Transcription:
Text Transcription:
f(y)=my^m-1 over alpha e^-ym/alpha, 0</=y<infinity, alpha, m>0
m=2
Questions & Answers
QUESTION:
The random variable 𝑌, with a density function given by
\(f(y)=\frac{m y^{m-1}}{\alpha} e^{-y^{m} / \alpha}, \quad 0 \leq y<\infty, \alpha, m>0\)
is said to have a Weibull distribution. The Weibull density function provides a good model
for the distribution of length of life for many mechanical devices and biological plants and
animals. Find the mean and variance for a Weibull distributed random variable with \(m=2\).
Equation Transcription:
Text Transcription:
f(y)=my^m-1 over alpha e^-ym/alpha, 0</=y<infinity, alpha, m>0
m=2
ANSWER:
Solution
Step 1 of 2
We have find mean and variance of a weibull distribution with m=2
Given that m=2
We know that mean=
=
=
Let u=
=
=
=
Note that
=