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4. Suppose we conduct independent Bernoulli experiments with probability of success p once every hour. We track the number of successes over time. Let T , 2, 3,...) (a) Define the state of this process at time t, Y(t) (b) What is the state space at time t? (c) What distribution would each Y(t) have? (d) How are the random variables X(t) (from the Bernouli process) and Y(t) related? (e) What would a plot of a realization of this process look like? (f) Provide an example of a realization of this process assuming T = 5

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