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Let $X$,$Y$ be independent and identically distributed continuos random variables. $X$ is distributed according to a Gaussian distribution with pdf ${f_g}_X(x;\mu,\sigma)$, while $Y$ according to a uniform distribution with pdf ${f_u}_Y(y;a,b)$ in the interval $[a,b]$. What is the joint probability density function?

Since $X$,$Y$ are continuous and indipendent from each other, is th joint pdf the product of the two, even if the two distributions are different? This way: $f_{XY}(x,y) = {f_g}_X(x;\mu,\sigma) \cdot {f_u}_Y(y;a,b)$

I'm really not sure about this, I'd need a clarification.

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