Originally Posted by

**hunkydory19** A variable $\displaystyle Y \in [0..\infty) $ has probability density

P(Y) = exp(-Y)

I'm trying to find the probability distribution of U = 2Y + 5, so I have done:

$\displaystyle P_y(y) = P_x(h(y))\frac{dh}{dy} $

$\displaystyle Y = h(U) = \frac{U - 5}{2} ; \frac{dh}{du} = \frac{1}{2} $

So $\displaystyle P(U) = \frac{1}{2} exp \frac{5 - U}{2} $

Could anyone please tell me if this is right or are probability density and probability distribution different things? I've looked up the defintions but I'm still confused.

Thanks in advance!