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Let the number of tropical cyclones per year in the Atlantic Basin (

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Answer #1

Let X be the number of tropical cyclones per year. The probability mass function (PMF) of X is

$p_X(x)=\frac{1}{11},x\in \{5,6,...,15\}$

the expectation of X is

The probability that any given tropical cyclone turns into a major hurricane is 0.30

Let Y|X be the number of major hurricanes given X number of tropical cyclones. We can say that Y|X has a Binomial distribution with parameters, number of trials (is the number of tropical cyclones) n=X and success probability (the probability that a tropical cyclone turns into a major hurricane) p=0.30.

Hence we have the following hierarchy.

the expected number of major hurricanes per year (

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Answer 1

Let X be the number of tropical cyclones per year. The probability mass function (PMF) of X is

$p_X(x)=\frac{1}{11},x\in \{5,6,...,15\}$

the expectation of X is

The probability that any given tropical cyclone turns into a major hurricane is 0.30

Let Y|X be the number of major hurricanes given X number of tropical cyclones. We can say that Y|X has a Binomial distribution with parameters, number of trials (is the number of tropical cyclones) n=X and success probability (the probability that a tropical cyclone turns into a major hurricane) p=0.30.

Hence we have the following hierarchy.

the expected number of major hurricanes per year (