a) Let Xbe a random variable with uniform distribution on the interval (a, b). Find its moment generating function 272 b) The random variable X has the following moments: E(X") n =1,2,... . n1 Find the moment generating function of X and identify the distribution of X. Hint: Use the Taylor expansion of etX to find the moment generating function, and use problem a) to identify the distribution

a) Let Xbe a random variable with uniform distribution on the interval (a, b). Find its moment generating function 272 b) The random variable X has the following moments: E(X") n =1,2,... . n1 Find the moment generating function of X and identify the distribution of X. Hint: Use the Taylor expansion of etX to find the moment generating function, and use problem a) to identify the distribution

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

show every mynute step in detail for problem (b)

a) Let Xbe a random variable with uniform distribution on the interval (a, b). Find its
moment generating function
272
b) The random variable X has the following moments: E(X")
n =1,2,... .
n1
Find the moment generating function of X and identify the distribution of X. Hint: Use
the Taylor expansion of etX to find the moment generating function, and use problem a)
to identify the distribution

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