Question: 1.5.3 Suppose that X is a discrete random variable having the geometric distribution whose probability mass function is p.k/ D p.1????p/k for k D 0;1;

1.5.3 Suppose that X is a discrete random variable having the geometric distribution whose probability mass function is p.k/ D p.1????p/k for k D 0;1; : : : :

(a) Determine the upper tail probabilities PrfX > kg for k D 0;1; : : : .

(b) Evaluate the mean via E[X] D 6k0 PrfX > kg.

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