Let X be the number of major storms in a particular state in a given year. The probability of having no major storms is 0.50, of one major storm is 0.30, of two major storms is 0.10, of three major storms is 0.08, and of four major storms is 0.02 (there have never been more than 4 major storms in this state in a given year).
a) Write down the probability distribution of X in table form, and also check to make sure it is a valid probability distribution.
b) Find the expected number of major storms in a given year, and the standard deviation of the number of storms in a given year.
c) Find the probability that there is at least 1 storm in a given year.
d) If there was more than 1 storm, nd the probability that there were 3 storms.