Suppose X1, X2, X3, X4, and so forth is a Bernoulli process with p the probability of success. Suppose Sn is the number of successes on the first n trials. Suppose Tk is the time of the kth.
A) The event {T2=4, T3=5} can occur in exactly 3 ways- each involving the first 5 trials only (the rest of the trials are irrelevant). List the 3 ways and give their probabilities.
B) Calculate P{T2=4, T3=5}
C) The event {S5= 2, T2=3} can occur in exactly 2 ways - each involving the first 5 trials only ( the rest of the trials are irrelevant). List the two ways and give their probabilities.
D). Calculate P{S5 = 3, T2=3}.
E) The event {S5=3 T2=3} can occur in exactly 4 ways - each involving the first 5 trials only ( the rest of the trials are irrelevant). List 4 ways and give their probabilities.
F) Calculate P{S5= 3, T2=3}.