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.

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Mathematics

Smirk

29 September, 10:36

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.

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Phillip Galloway · Answer 1

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