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OpenStudy (kirbykirby):
Assume all the random variables are mutually independent. Let \(S_n=X_1+X_2+...+X_{n-1}+X_n\) Given this expression: \(P(X_n=j\mid S_n=k)P(S_n=k)\) I have the following steps, but I don't know how they got to the last line: \(=P(X_n=j,S_n=k)\\ =P(X_n=j)P(S_{n-1}=k-j)\)
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