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1) Consider a random sample X₁, X2, ..., Xn from a population distributed with the following mass function: f(x) = 3xe-3 x! 0, for x = 0,1,...,00 elsewhere a) What is the mean and variance of a statistic Y = Σ₁X₁? 10 Li=X? 10 1 10 b) What is the mean of the statistic Y = [²º₁X? c) Find the probability distribution function of Y = Zi=1 d) What is the probability that Y = ₁X₁ is at least 3? 10 1₁X₁. i=1

1) Consider a random sample X₁, X2, ..., Xn from a population distributed with the following mass function: f(x) = 3xe-3 x! 0, for x = 0,1,...,00 elsewhere a) What is the mean and variance of a statistic Y = Σ₁X₁? 10 Li=X? 10 1 10 b) What is the mean of the statistic Y = [²º₁X? c) Find the probability distribution function of Y = Zi=1 d) What is the probability that Y = ₁X₁ is at least 3? 10 1₁X₁. i=1

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 19E
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K 1) Consider a random sample X₁, X₂, ..., Xn from a population distributed with the following mass function: 21 f(x) = (3x e Let Y x! 0, 0,1, elsewhere for x a) What is the mean and variance of a statistic Y = Σ1₁X₁? Xi? b) What is the mean of the statistic Y = [²º₁ 10 c) Find the probability distribution function of Y = Σ1º₁ X₁. i=1 d) What is the probability that Y = Σ1º₁ X¡ is at least 3? Y Y y be an independent and identically random variables following a V
Transcribed Image Text:K 1) Consider a random sample X₁, X₂, ..., Xn from a population distributed with the following mass function: 21 f(x) = (3x e Let Y x! 0, 0,1, elsewhere for x a) What is the mean and variance of a statistic Y = Σ1₁X₁? Xi? b) What is the mean of the statistic Y = [²º₁ 10 c) Find the probability distribution function of Y = Σ1º₁ X₁. i=1 d) What is the probability that Y = Σ1º₁ X¡ is at least 3? Y Y y be an independent and identically random variables following a V
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