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**CountingPenguins** Let X and Y be independent exponential random variables with $\displaystyle E(X)=2.5$ and $\displaystyle E(Y)=3.5.$

Find the joint probability distribution $\displaystyle f(x,y)$.

I know that the probability density function for X is $\displaystyle \frac{2}{5}e^{\frac{-2x}{5}$ for x>0 and 0 otherwise.

also

I know that the probability density function for Y is $\displaystyle \frac{2}{7}e^{\frac{-2x}{7}$ for x>0 and 0 otherwise.

I am not sure about jointly. Do I simply multiply them together?

Find $\displaystyle P(X+Y>15)$.

I have no idea how to begin this part, although I know the answer is .04.

Can anyone help?