Question 3 [10 marks]. Suppose that X, Y and Z are statistically independentrandom variables, each of them with a x²(2) distribution.(a) Find the moment generating function of U = X + 3Y + Z. State clearly andjustify all steps taken.(b) Calculate the expectation E(U) using the moment generating function.

a.)Moment Generating Function of U Define of the Moment Generating Function: The MGF of a random…

Answered: Question 3 [10 marks]. Suppose that X,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 22E

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Similar questions

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A random variable X has a N(0,1) distribution. Use the moment generating function of X to compute (a) the third and (b) fourth moments of X, i.e., E(X³) and E(X4).
(Revision.) Let X = Wo.5 + 0.5W1 – 2W2 – W3, where (W1, t > 0) is standard BM. Find the expectation E(X²).
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3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?
C1. Let X be a continuous random variable with PDF f(x) = ? (2 – a) for –1 1)? (c) Calculate the expectation and variance of X. (d) Let Y (X2 – 1). What is the expectation of Y?
please answer in a detailed way/solution. LETTER A & B
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