Answered: a) b) c) Calculate the probability that… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Question

Suppose that X₁, X₂, X3 are mutually independent random variables with the respective moment
2
generating functions, Mx, (t) = e²¹², Mx₂ (t) = e²t + 3t², and Mx₂(t) = (¹₂) 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.
c)
Find the mean and variance of the statistic Y, if
i) Y = Σ=1 X.
2
ii) Y = 4X¹²
4X₁²
X3
d)
if y = X₁² + X3, what is the probability that Y is at most 12.833?
2X1
e)
Find the value of such that P(Y > T) = 0.005, for Y
=

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