Moment generating functions (intro)
Probability theory · Mathematics
Study notes
Q: X is Bernoulli(p). Find its mgf and use it to get E(X). M(t) = E(e^(tX)) = e^(t·0)(1-p) + e^(t·1)p = (1-p) + p e^t. M'(t) = p e^t. M'(0) = p = E(X). Correct! M''(t) = p e^t, M''(0) = p = E(X^2). Var = p - p^2 = p(1-p). Correct!