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Suppose that X₁, X2, X3 are mutually independent random variables with the respective moment generating functions, Mx, (t) = est¹², Mx₂(t) = e²t + 3t², and Mx, (t) = (-)². a) Calculate the probability that X₂ is between 2 and 4, P (2 < X₂ < 4). State with parameter(s) the probability distribution of Y = X₁ + X₂. b)

Suppose that X₁, X2, X3 are mutually independent random variables with the respective moment generating functions, Mx, (t) = est¹², Mx₂(t) = e²t + 3t², and Mx, (t) = (-)². a) Calculate the probability that X₂ is between 2 and 4, P (2 < X₂ < 4). State with parameter(s) the probability distribution of Y = X₁ + X₂. b)

MATLAB: An Introduction with Applications
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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Suppose that X₁, X₁, X3 are mutually independent random variables with the respective moment generating functions, Mx₂(t) = e²¹², Mx₂(t) : 1 = µ2t + 3t², and Mx₂ (t) = (--)². 1-2t, a) Calculate the probability that X₂ is between 2 and 4, P(2 < X₂ < 4). b) State with parameter(s) the probability distribution of Y = X₁ + X₂. Find the mean and variance of the statistic y, if c) i) Y = Σ=1X. d) e) 4X₁² X3 if Y = X₁² + X3, what is the probability that Y is at most 12.833? ii) Y = Find the value of τ such that P(Y > t) T = 0.005, for Y = 2X₁ √X3
Transcribed Image Text:Suppose that X₁, X₁, X3 are mutually independent random variables with the respective moment generating functions, Mx₂(t) = e²¹², Mx₂(t) : 1 = µ2t + 3t², and Mx₂ (t) = (--)². 1-2t, a) Calculate the probability that X₂ is between 2 and 4, P(2 < X₂ < 4). b) State with parameter(s) the probability distribution of Y = X₁ + X₂. Find the mean and variance of the statistic y, if c) i) Y = Σ=1X. d) e) 4X₁² X3 if Y = X₁² + X3, what is the probability that Y is at most 12.833? ii) Y = Find the value of τ such that P(Y > t) T = 0.005, for Y = 2X₁ √X3
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