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a) Suppose that a r.v. Y has Exponential Distribution Y-Exp(1). Find the distribution of W = BY for some ß> 0. ● ● Fy(y) = F (w) - Pr(W ≤w) =_ Definition: A random variable W is said to have the Weibull distribution with parameters B and k if its cdf is of the form Fw (w)=1-e b) Write down the pdf of W fw (w) = (Fw (w)) 0 for w> 0.. w>0 otherwise

a) Suppose that a r.v. Y has Exponential Distribution Y-Exp(1). Find the distribution of W = BY for some ß> 0. ● ● Fy(y) = F (w) - Pr(W ≤w) =_ Definition: A random variable W is said to have the Weibull distribution with parameters B and k if its cdf is of the form Fw (w)=1-e b) Write down the pdf of W fw (w) = (Fw (w)) 0 for w> 0.. w>0 otherwise

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 43CR
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a) Suppose that a r.v. Y has Exponential Distribution Y - Exp(1). Find the distribution of W = B√Y for some ß> 0. • Fy(y)=_ ● Fw (w)= Pr(W ≤w) = Definition: A random variable W is said to have the Weibull distribution with parameters B and k if its cdf is of the form F₁ (w) = 1-e, for w> 0.. b) Write down the pdf of W fw (w) = (F₁(w)) = { 0 w>0 otherwise
Transcribed Image Text:a) Suppose that a r.v. Y has Exponential Distribution Y - Exp(1). Find the distribution of W = B√Y for some ß> 0. • Fy(y)=_ ● Fw (w)= Pr(W ≤w) = Definition: A random variable W is said to have the Weibull distribution with parameters B and k if its cdf is of the form F₁ (w) = 1-e, for w> 0.. b) Write down the pdf of W fw (w) = (F₁(w)) = { 0 w>0 otherwise
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