Assume that X is discrete, with possible values {a i ; i ≥ 1) and probabilities Pr{X = a i } = p i . Let X r be the corresponding tilted random variable as defined in Exercise 9.5 Exercise 9.5 Define...

Assume that X is discrete, with possible values {a_i; i ≥ 1) and probabilities Pr{X = a_i} = p_i. Let X_r
be the corresponding tilted random variable as defined in Exercise 9.5

Exercise 9.5

Define ϒ(r) as ln [g(r)] where g(r) = E [exp(rX)]. Assume that X is discrete