Question
Derive the cof for the Weibull distribution. [Hint: In the definition of a cdf, make the transformation $z=y^{\beta} .$
Step 1
Step 1: First, we are given the probability density function (pdf) of the Weibull distribution as follows: \[f(x;\alpha,\beta) = \alpha\beta x^{\beta-1}e^{-\alpha x^\beta}\] where $x > 0$ and $0$ otherwise. Show more…
Show all steps
Your feedback will help us improve your experience
Amany Waheeb and 99 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Derive the cdf for the Weibull distribution. [Hint: In the definition of a cdf, make the transformation $\left.z=y^{\beta} .\right]$
Some Continuous Probability Distributions
VVeibull Distribution
Let $X$ have a Weibull distribution. Verify that $\mu=\beta \Gamma(1+1 / \alpha) .[$Hint$:$ In the integral for $E(X)$ ) make the change of variable $y=(x / \beta)^{\alpha},$ so that $x=\beta y^{1 / \alpha} . ]$
Continuous Random Variables and Probability Distributions
Other Continuous Distributions
Derive the cdf for an exponential distribution with parameter λ.
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD