is a random variable with weibull distribution given with

Let and .

Show that has exponential distribution and find value of parameter .

I believe that should be expressed in terms of , but I don't know where to start.

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- Jun 19th 2010, 02:19 AMlosm1Weibull & Exponential distribution
is a random variable with weibull distribution given with

Let and .

Show that has exponential distribution and find value of parameter .

I believe that should be expressed in terms of , but I don't know where to start. - Jun 19th 2010, 03:29 AMSpringFan25
you have the right approach

Lets find P(Y<y)

Find (or look up) F(x) then subsititute these values in to get the CDF of Y. Hopefully it will look like an exponential distribution. - Jun 19th 2010, 03:30 AMmr fantastic
Since you know in advance that the answer is going to be a well-known distribution, a simple approach would be to calculate the moment generating function of Y ....

**But**if you're determined to use a distribution function approach, then you should start by noting that the cdf of Y is:

since the support of X is .

Now set up the required integral (no need to integrate by the way ....) and then differentiate using the chain rule and the Fundamental Theorem of Calculus. - Jun 19th 2010, 04:14 AMlosm1