(a) Discuss the method of determination of probability that at least seven of the events A1, A2, A3, A20 occur simultaneously. State a problem where you can use the above result. (b) State and prove Bayes' theorem. Construct a problem with four events E, F, F2 and F3, where F, F2 and F3 are mutually exclusive and exhaustive. Solve the problem using Bayes' theorem. (c) Distinguish between discrete and continuous random variables. Define a probability density function. Suggest, giving justifications, a probability density function of a random variable X where f(x) = 5 for at least one x. Find Skewness (B-coefficient) and Kurtosis (2-coefficient) of X.