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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 32E

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STATISTICAL INFERENCE

Suppose that ?1, ?2, ?3 are mutually independent random variables with the respective moment
generating functions

Suppose that X₁, X₂, X3 are mutually independent random variables with the respective
2
generating functions, Mx, (t) = e²¹², Mx₂(t) = µ²t + 3t², and Mx, (t) = (₁-¹)².
1-2t.
a)
b)
c)
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.
Find the mean and variance of the statistic Y, if
i)_ Y = Σ=1 X.
4X₁²
X3
if Y = X₁² + X3, what is the probability that Y is at most 12.833?
ii) Y
=
d)
2X1
e) Find the value of such that P(Y > t) = 0.005, for Y =
T
Pall

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