Question

Suppose we conduct independent Bernoulli experiments with probability of success p once every hour. We track the number of successes over time. Let T= {1,2,3,...}.

a) Define the state of this process at time t, Y(t).

b) What is the state space at time t?

Answer 1

a)

The state of this process at time t, Y(t) is the total number of successes from Bernoulli experiments till time t.

By definition of binomial distribution, Y(t) ~ Binomial(t, p)

b)

At time t, we can have from 0 to t successes.

The state space at time t is {0, 1, 2, 3, ..., t}