The lifetime of a product is where x has an exponential distribution with mean 1. I need to find the distribution function and pdf of Y.
For the pdf I got . Can this be simply integrated to get the distribution function F(Y) to equal ? I obviously need the for something, but I'm not sure how to incorporate it besides subbing
the pdf of y is equal to the pdf of x multiplied the derivative of THE CHANGE OF VARIABLES
Dependent variables and change of variables
thank you for the link. I found this under change of variables. I'm sure I am mistaken, but I though the following means the derivative of the pdf of y equals the derivative of the pdf of x: That would then mean they are equal and both , which can't be right. I apologize for being so confused.
so would be my distribution function F(y)?
After differentiating this messy equation I have the p.d.f. f(y)= .
This all looks too messy to be correct. Can somebody help point me in the right direction? This is confusing me so much. The more I read, the more confused I am getting. Thank you so much for your help!
I obviously should have used
multiplying the two together, I got which looks a little better but still doesn't seem right. Any help would be extremely appreciated.
There's more than enough help been given to answer this question.