Question

It is reasonable to model the number of winter storms in a season as with a Poisson random variable. Suppose that in a good year the average number of storms is 5, and that in a bad year the average is 6. If the probability that next year will be a good year is 0.3 and the probability that it will be bad is 0.7, find the expected value and variance in the number of storms that will occur. expected value.

Answer 1

Answer:

If the probability of a good year is 0.3 and the probability of a bad year is 0.7, we can multiply these values by the number of storms that each one represents. So (0.3*5)+(0.7*6)= 5.7, this is the number of storms expected for the next year. For the variance, we need to do a summary between the average and the data collected, so {[(5-5.7)^2]+[6-5.7]^2}/2 = variance = 0.29, this means that the expected number of storms fro the nex year will be 5.7 +- 0.29.

Finally, the average number of expected storms for the next year is 5.7, with a variance of 0.29