An actuary is studying hurricane models. A year is classiﬁed as a high, medium, or low hurricane year with probabilities 0.1, 0.3, and 0.6, respectively. The numbers of hurricanes in high, medium, and low years follow Poisson distributions with means 20, 15, and 10, respectively. Calculate the variance of the number of hurricanes in a randomly selected year

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09-12-2022
Mathematics

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An actuary is studying hurricane models. A year is classiﬁed as a high, medium, or low hurricane year with probabilities 0.1, 0.3, and 0.6, respectively. The numbers of hurricanes in high, medium, and low years follow Poisson distributions with means 20, 15, and 10, respectively. Calculate the variance of the number of hurricanes in a randomly selected year

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rafikiedu08 rafikiedu08 · Answer 1 · 2022-12-17T05:56:14-05:00

The variance of the number of hurricanes in a randomly selected year is 12.5 .

Mean number of hurricanes in a randomly selected year =

0.1 × 20 + 0.3 × 15 + 0.6 × 10 = 12.5

Now, since the sum of independent Poisson random variables also follows Poisson distribution.

Thus, the variance of the number of hurricanes in a randomly selected year = Mean = 12.5

In both statistics and probability theory, variance is the predicted squared deviation of a binomial distribution from its sample proportion or sample mean.

Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance. A few ideas that involve variance are descriptive research, statistical inference, testing hypotheses, goodness of fit, and Monte Carlo sampling.

The variance of a set of uncorrelated explanatory variables is equal to the sum of their variances, making it easier to manipulate mathematically than other measures of dispersion like anticipated absolute deviation.

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