Probability and Statistics II week 5
MOMENT GENERATING FUNCTION (m.g.f) The moment generating function (m.g.f) of a random variable X is defined as: is the expected value of . We are required to show that: and Proof We know that is differentiable. when t = 0; when t = 0; But we know that; Example 2.8 Consider the random variable X whose p.d.f. is where is the parameter of the distribution. (a) Obtain the moment generating function of X. (b) Hence obtain the mean and variance of X. Solution (a) Thus the moment generating function of X is . (b) where at t = 0, Next, variance of X is given by So at t = 0, Hence
Escuela, estudio y materia
- Institución
- Probability
- Grado
- Probability
Información del documento
- Subido en
- 30 de mayo de 2023
- Número de páginas
- 10
- Escrito en
- 2022/2023
- Tipo
- Notas de lectura
- Profesor(es)
- Prof kinyanjui
- Contiene
- Week 5
Temas
-
moment generating function mgf
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