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Chapter 5: Q. 5.25 (page 216)

Let Y=X-饾湀饾浖.

Show that if X is a Weibull random variable with parameters 谓, 伪, and 尾, then Y is an exponential random variable with parameter 位 = 1 and vice versa.

Short Answer

Expert verified

The above statement is proved.

Step by step solution

01

Given information

We are assuming thatXis a Weibull with parameters饾湀,饾浖and饾浗

02

Calculation

We have

PX-饾湀饾浖饾浗鈮�x=PX-饾湀饾浖鈮�x1饾浗=PX鈮�饾湀+饾浖x1饾浗=1-e-x

which is nothing but the CDF of exponential distribution.

Therefore it's proved that Ywill follow exponential distribution with parameter饾浑=1

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