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Define (a) stochastic process; (b) random variable; (c) discrete random variable; and (d) probability distribution.

Without using formulas, explain the meaning of (a) expected value of a random variable; (b) actuarial fairness; and (c) variance of a random variable.

What are the parameters of a binomial distribution? (b) What is the mean of a binomial distribution? The standard deviation? (c) When is a binomial skewed right? Skewed left? Symmetric? (d) Suggest a data-generating situation that might be binomial.

What are the parameters of a Poisson distribution? (b) What is the mean of a Poisson distribution? The standard deviation? (c) Is a Poisson ever symmetric? (d) Suggest a data-generating situation that might be Poisson.

When are we justified in using the Poisson approximation to the binomial? (b) Why would we want to do this approximation?

Explain a situation when we would need the hypergeometric distribution. (b) What are the three parameters of the hypergeometric distribution? (c) How does it differ from a binomial distribution?

When are we justified in using (a) the Poisson approximation to the binomial? (b) The binomial approximation to the hypergeometric?

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Category:- Statistics and Probability
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