Consider the following variation on the Bernoulli process: the first two trials are not independent. However, the following facts are known:
P{X1=1}=0.9; P{X2=1 | X1=1}=0.8; P{X2=1|X1=0}= 0.95
For all the remaining trials starting at X3, the probability of success is 0.99. All the remaining trials are independent of X1 and X2.
a. Calculate the probability that X1+ X2 +X3 is equal to 2.
b. Derive the distribution of the number of the trial at which the first success appears.
c. Suppose T2 is the number of the trial at which the second success occurs. Calculate the probability that T2 is equal to 3.
d. Produce and display general formulas for the probability mass function of t2.