Probability and Statistics II week 8
1.1.1. GEOMETRIC (PASCAL) DISTRIBUTION A random variable X is defined to have a geometric distribution, if the discrete probability distribution function (p.d.f) of X is given by 0<p<1. p = probability of success and q is the probability of failure. This distribution occurs in real life, in situations where we have say a random variable X representing the number of trials required before the first success, then X has a geometric distribution. The Mean, Variance and Moment generating function of the Geometric Distribution We first work out the m.g.f. which will in turn be used to obtain the mean and variance expressions. By definition; Next, we know that at t = 0; we have Next we work out Var (x) We know that Using product rule to differentiate the above expression, we get Let At t = 0; But
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- Institution
- Probability
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- Uploaded on
- May 30, 2023
- Number of pages
- 20
- Written in
- 2022/2023
- Type
- Class notes
- Professor(s)
- Prof kinyanjui
- Contains
- Week 7
Subjects
- the mean
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111 geometric pascal distribution
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variance and moment generating function of the geometric distribution
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sampling with and without replacement
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112 hypergeometric distribution
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317 t
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