# Thread: distribution function and p.d.f.

1. ## distribution function and p.d.f.

The lifetime (in years) of a product is $\displaystyle Y=5X^{0.7}$ where X has an exponential distribution with mean one. Find the distribution function and p.d.f. of Y.

Thank you in advance.

2. Originally Posted by calabrone
The lifetime (in years) of a product is $\displaystyle Y=5X^{0.7}$ where X has an exponential distribution with mean one. Find the distribution function and p.d.f. of Y.

Thank you in advance.
I'd calculate the cdf of Y and then differentiate to get the pdf:

$\displaystyle F(y) = \Pr(Y < y) = \Pr(5 X^{0.7} < y) = \Pr \left( X^{0.7} < \frac{y}{5} \right) = \Pr \left( X < \left( \frac{y}{5} \right)^{10/7} \right)$ $\displaystyle = \int_0^{\left( \frac{y}{5} \right)^{10/7}} g(x) \, dx$

where $\displaystyle g(x)$ is the pdf of X.

3. Originally Posted by calabrone
The lifetime (in years) of a product is $\displaystyle Y=5X^{0.7}$ where X has an exponential distribution with mean one. Find the distribution function and p.d.f. of Y.

Thank you in advance.
Popular question. Asked and answered (in different ways) in the following threads:

http://www.mathhelpforum.com/math-he...tial-dist.html

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

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

Thread closed.