The lifetime of a product is Y = 5X^0.7 , where X has an exponential dist. with mean = 1

Find the distribution function and pdf of Y

I'm not even sure where to start here...

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- Jul 10th 2008, 02:35 PMamor_vincit_omniaAnother exponential dist.
The lifetime of a product is Y = 5X^0.7 , where X has an exponential dist. with mean = 1

Find the distribution function and pdf of Y

I'm not even sure where to start here... - Jul 10th 2008, 02:57 PMmeymathis
The lifetime of a product is Y = 5X^0.7 , where X has an exponential dist. with mean = 1

So the cdf,

The last expression is in the form of the CDF of an exponential. ( ) And so

To get the pdf, just take the derivative of the CDF.... - Jul 10th 2008, 04:22 PMamor_vincit_omnia
I did that, but it's not the correct answer.

Unless I'm doing something wrong

here's the answer:

[10/7*y^(3/7)*e^(-y/5)^10/7] / 5^(10/7)

Looks like your answer is pretty close, so I assume it's me doing something wrong. Thanks for the help - Jul 10th 2008, 08:33 PMmeymathis
derivative of the CDF:

derivative of the sum is sum of the derivatives

derivative of constant is 0

1/.7 = 10/7

Now (derivative of exp with chain rule). So

Then

which is what you had

Quote:

[10/7*y^(3/7)*e^(-y/5)^10/7] / 5^(10/7)

- Jul 10th 2008, 09:05 PMamor_vincit_omnia
Yea, I actually figured it out like an hour ago. Been too many years since calculus; thanks for all your help!

- Apr 28th 2009, 03:59 AMmr fantastic
Popular question. Asked and answered (in different ways) in the following threads:

http://www.mathhelpforum.com/math-he...ion-p-d-f.html

http://www.mathhelpforum.com/math-he...ction-f-x.html

http://www.mathhelpforum.com/math-he...-lifetime.html