Consider the following density function:fa(z) = {0z2 0,I < 0.5eFind the moment generating function of X random variable.O a. 4 (t) = , assuming that t < 2%3|O b. Hz (t) = , assuming that t < 5O c. Hz (t) = , assuming that t < 5O d. 4 (t) = , assuming that t < 22-tO e. z (t) = , assuming that t < 52-5t

The moment generating function is defined as E(etx)

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Probability

Find the moment generating function of X random variable.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Consider the following density function:
fa(z) = {0
z2 0,
I < 0.
5e
Find the moment generating function of X random variable.
O a. 4 (t) = , assuming that t < 2
%3|
O b. Hz (t) = , assuming that t < 5
O c. Hz (t) = , assuming that t < 5
O d. 4 (t) = , assuming that t < 2
2-t
O e. z (t) = , assuming that t < 5
2-5t

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