3. find the distributions of the random variables that have each of the followingmoment generating functions:et2-et1a) m(t) ==b) m(t) = e²(et-1)c) Using results in (a) and (b), Find the E(Y) and V (Y)?Suppose that Y is a random variable with moment-generating function m(t) If

The moment-generating functions are as follows: (a) mt=et2-et (b) mt=e2et-1

Answered: find the distributions of the random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Consider two random variables X₁ and X2 whose joint pdf is given by for x₁0, x2 > 0, x₁ + x2 < 2, { Find the pdf of Y = X₂ - X₁. f(x1, x₂) = NIT otherwise.
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Establish the following: 0P (E)1 , P (A u B) = P (A) + P (B) – P (A n B) , P (A) = 1 – P (A’) ii The probability that a boy with a catapult hits target A is 2/3and that he hits target B is ¾. Given the probability of hitting both targets to be 1/2, find the probability that he (a) hits at least one of the targets (b) does not hit any. iii What is the probability of having at least one 6 in three throws with a dice?
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2. Assume X ~ Exp(0), so that its pdf is 1 f(x; 8) x > 0,0 < 0 < o. e We have 5 samples, 1,2,3,4, and, 5, under Exp(0). Find the maximum likelihood estimator of 0 using the five samples.
Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
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1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.

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find the distributions of the random variables that have each of the following moment generating functions: a) m(t) == 2-et b) m(t) = e²(e¹-1) c) Using results in (a) and (b), Find the E(Y) and V (Y)?