X denotes a random variable with pdf
let , find the cdf of Y and hence the pdf of Y and cov(X,Y).
I know that to find the pdf from the cdf we differentiate, but I'm not sure how to handle to transformation to
I can understand the method of distribution functions better....
I've just noticed the negative cdf...sometimes I get caught up in the calculating and don't use common sense!
Perhaps I should give the question in full....
the pdf is given above, I then have to find the cdf(by integrating the pdf given) then the transformation is given and I have to then find the cdf of Y and the pdf of Y, and finally the covariance of (X,Y)....
These TWO techniques are the same. IF you differentiate...
wrt the variable y (this is not a random variable, this is calc 1) you get
The general formula, which is in most books is
but since x>0 we have
Thanks.
So given the pdf ....
The replies have helped alot, however I'm trying to find the cdf from this pdf then the transformation and then find the cdf of Y and so then the pdf of Y....
1)What would the cdf be as I get a negative answer as I shown a couple posts ago..??
2)What is the process to obtaining the cdf of Y?
3)and finally then the pdf of Y?