Question: can you explain? Theorem 3.5 The geometric (p) random variable X has expected value E[X] = 1/p. Proof Let q = 1 - p. The

can you explain?

Theorem 3.5 The geometric (p) random variable X has expected value E[X] = 1/p. Proof Let q = 1 - p. The PMF of X becomes pq x-1 Px (x) = x = 1, 2, .. . 0 (3.43) otherwise. The expected value E[X ] is the infinite sum EX] = xPx (2) = xpq. -1 (3.44) = x=1 Applying the identity of Math Fact B.7, we have DO EX] =P P q xq xq (3.45) q 1 -q2 =

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