(Solved): 9. Let \( X_{n} \) be a sequence of independent, identically distributed Bernoulli random variable ...

9. Let \( X_{n} \) be a sequence of independent, identically distributed Bernoulli random variables with \( p=1 / 2 \). Let \( S_{n} \) be the number of 1 's in the first \( \mathrm{n} \) trials, i.e., \( S_{n}=X_{1}+X_{2}+\cdots+X_{n} .(9 \) points \( ) \) (1) What is the probability \( P\left(X_{n}=1\right) \) ? (2) What is the mean function of \( S_{n} \) ? (3) What is the probability \( P\left(S_{n}=k\right) \) ?