at least 69 tropical cyclones affected the state of texas si

at least 69 tropical cyclones affected the state of texas since 1980. given that the number of hurricanes is poisson distributed with the mean of either 1 in a good weather year or 3 in a bad weather year. suppose that any year\'s weather condition depends on the previous year\'s condition. suppose that

*a good weather year is followed by a good weather year with probability .5;

*a bad weather year is followed by a bad weather year with probability .6.

Suppose that this year 2013 is a good year.

(a) Model this markov chain and find the one step transition matrix.

(b) find the expected number of hurricanes in year 2015

(c) find the probability that there are no hurricanes in year 2016

(d) find the long-run average number of hurricanes per year.

Solution