Let X represent the lifetime of a component, in weeks. Let Y represent the lifetime of
Chapter 4, Problem 27(choose chapter or problem)
Let represent the lifetime of a component, in weeks. Let
represent the lifetime of the component in days, so \(Y=7 X\). Suppose \(X \sim \operatorname{Exp}(\lambda)\)
a. Let \(F_{Y}\) be the cumulative distribution function of and let \(F_{X}\) be the cumulative distribution function of
Show that \(F_{Y}(y)=1-e^{-\lambda y / 7}\). [Hint: \(F_{Y}(y)=P(Y \leq y)=P(7 X \leq y)=P(X \leq y / 7)\)]
b. Show that \(Y \sim \operatorname{Exp}(\lambda / 7)\) [Hint: Find the probability density function of by differentiating \(F_{Y}(y)\)]
Equation Transcription:
Text Transcription:
Y=7X
X \sim Exp(lambda)
FY
FX
FY(y)=1-e-lambda y/7
FY(y)=P(Y \leq y)=P(7X \leq y)=P(X \leq y/7)
Y \sim Exp(lambda/7)
FY(y)
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