A1. (i) Let X be a random variable with probability mass function ( pmf )
Determine the probability generating function of X.
(ii) Suppose that the probability generating function of a random variable X is given by
Determine the probability mass function of X. [5 marks]
(Hint: You may use the formula: P1
A2. Let Zn, n ≥ 0 be a branching process with offspring distribution
(i) Find the offspring generating function G(s) and the expectation of N. [4 marks]
(ii) Determine the probability generating function of Z2 and write down P(Z2 = 3).
Please see the attached file for the fully formatted problems.
keywords: pmf, p.m.f., pgf, p.g.f.
Random Variables, Probability Mass Functions, Probability Generating Functions and Offspring Generating Functions are investigated. The solution is detailed and well presented.