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Determine the probability generating function of x.

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Reference no: EM13957233

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.

Reference no: EM13957233

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