Question

STAT 135 19. Jack goes to fish at 8 a.m everyday and catches fish according to a Poisson process with a mean 0.6 catches per hour. Let X1 be the number of fishes from 8 am to 9 am, and X2 be the number of catches from 9am to 11am.

1) Find the Probability P(X1+X2=5, X2= c) for c=0,1,2,3,4,5

2) Let Wi be the time, in hours, it takes Jack to catch i fish. Find the Probability P( W1≤ 1, W2 >3)； (W1≤ 1, W2 >3) can be in terms of X1, X2.

Answer 1