# The distribution of the product of two random variables

X=Normal(0,1) random var. Y=Uniform{-1,1} random var. Show that Z=X.Y is normal random variable.

• The conclusion is false. Did you perhaps mean to stipulate that $Y$ is a random variable that takes the values $\{-1,1\}$ with equal probability (of $1/2$ each)? Regardless, please consult our help center about asking questions and kindly tell us what attempts you have made at this question and where specifically you could use some help. – whuber Feb 5 '14 at 23:06
• @arke No, it is $U\{-1, +1\}$ – Dilip Sarwate Feb 6 '14 at 0:19
• arke, "$U(-1,1)$" without further adornment is generally taken to be a continuous uniform distribution between $-1$ and $1$ ... for which the statement is untrue. If you want a 50-50 chance of the values -1 and 1, you'd specify it differently. – Glen_b -Reinstate Monica Feb 6 '14 at 0:41