Discuss the following:
1. Define (a) stochastic process; (b) random variable; (c) discrete random variable; and (d) probability distribution.
2. Without using formulas, explain the meaning of (a) expected value of a random variable; (b) actuarial fairness; and (c) variance of a random variable.
6. (a) 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.
7. (a) 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.
9. (a) When are we justified in using the Poisson approximation to the binomial? (b) Why would we want to do this approximation?
10. (a) 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?
11. When are we justified in using (a) the Poisson approximation to the binomial? (b) The binomial approximation to the hypergeometric?