Thread: Probability density functions

If X1,X2 .....Xn are independent N(0,1) random variables, do the following
(1) Find the probability density function of U = X^2
HINT : The density function is F(u)= d/duP[X^2 <= u]

Ok so far i think it is
f(u) = d/du[1- P[x^2 > u]
= -d/duP[x^2 > u]

Is this right??

Originally Posted by frog

If X1,X2 .....Xn are independent N(0,1) random variables, do the following
(1) Find the probability density function of U = X^2
HINT : The density function is F(u)= d/duP[X^2 <= u]

Ok so far i think it is
f(u) = d/du[1- P[x^2 > u]
= -d/duP[x^2 > u]

Is this right??

With a bit of patience, if you search this subforum you will find the same sort of question has been done before. Personally, I'd do this one using moment generating functions (hint: the answer is a chi-square distribution).