Help find mean and variance please

Question

I have beeen asked to find the pdf of Y for this function. I get y(lamda)^(2)exp{((lamda x Y)^2)/2)}. I am having trouble finding the mean and variance. Can someone help? Thank you.

Y =P((2X/λ)^0.5), where X ∼ Exp(λ)

Answer 1

I think you've worded everything badly:

(1) What is your exact question? Are you given $X$ (a random variable) with exponential distribution and parameter $\lambda$, and are asked to work out the pdf of $Y$? If so, what is Y exactly? Remember that Y must be a random variable as well, so what does $P$ mean, where you've written $Y=P(\sqrt{\frac{2X}{\lambda}})$. Is there also a separate question asking to work out the mean and variance (of $X$, $Y$?)

(2) Your first expression says $y\lambda^2e^\frac{\lambda xY^2}{2}$. Here, you have used both $y$ and $Y$. You should always distinguish between the two - in general, $y$ is a variable (constant), whereas $Y$ is a random variable (function)

Re-word your question, and we may be able to help you