Question: Suppose that X is a random variable such that Pr[X = 4] = Pr[X = 10] 1/3 (a) Is it possible for Var[X] 1? (b)

Suppose that X is a random variable such that Pr[X = 4] = Pr[X = 10] 1/3

(a) Is it possible for Var[X] 1?

(b) Specify the PDF for X with the constraint above that has minimum variance.

(c) Suppose there are in total 12 independent traffic lights along Alex's route to work, among those independent traffic lights, each has probability of 0.4 to be a red light. Alex will be late to work if he encounters 8 or more red lights in a given day. Give an upper bound for that Alex will be late using the Chernoff bound.

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