Problem:

(a) Describe the difference between risk and uncertainty. Give an example to illustrate your answer.

(b) Name three common measures of risks and outline their potential benefits.

(c) Describe briefly, by making use of examples, the situation under which each of the following distributions is employed:

(i) The Normal distribution
(ii) The Triangular distribution
(iii) The Poisson distribution
(iv) The Lognormal distribution
(v) The Weibull distribution
(vi) The Pareto distribution

(d) In what ways is the Hypergeometric distribution different from the Binomial distribution?

(e) Describe the following two measures of shape: skewness and kurtosis. Illustrate examples of these two measures of shape.

(f) State Bayes' Theorem.

(g) Three machines and C produce 20%, 45% and 35% respectively of a factory's wheel nuts output. 2%, 1% and 3% respectively of these machines' outputs are defective.

(i) What is the probability that any wheel nut randomly selected from the factory's stock will be defective?

(ii) What is the probability that a randomly selected wheel nut comes from machine A if it is defective?