(Solved): correct answer please  Discrete convolution formula. Let \( X \) and \( Y \) be independent ran ...

Discrete convolution formula. Let \( X \) and \( Y \) be independent random variables with non-negative integer values. Show that: a) \( P(X+Y=n)=\sum_{k=0}^{n} P(X=k) P(Y=n-k) \). b) Find the probability that the sum of numbers on four dice is 8 , by taking \( X \) to be the sum on two of the dice, \( Y \) the sum on the other two.