$X,Y$ are random independent variables with normal distribution. Can we conclude that $XY$ has also normal distribution ?
I know definition of normal distributio, however I have a problem with it. Can you explain it ?
$X,Y$ are random independent variables with normal distribution. Can we conclude that $XY$ has also normal distribution ?
I know definition of normal distributio, however I have a problem with it. Can you explain it ?
Note that $XY =\frac{1}{4}\Big( (X+Y)^2 + (X-Y)^2 \Big)$. If $X$ and $Y$ have same mean and variance, say mean $0$ and variance $1$, then $(X+Y)^2$ and $(X-Y)^2$ are Chi-Square with one degrees of freedom. So $XY$ is a sum of Chi-Squares, which is not Gaussian.
P.S: I have deleted my previous answer because i assumed they were dependent and picked a counter example. Here is the case when $X$ and $Y$ are independent