independe n1 constitut- ing a random sample from an infinite population with the mean ₁ and the variance of and the other n2 constitut ing a random sample from an infinite population with the mean μ2 and the variance o2, then (a) E(X₁-X₂) = μ₁ −μ2; 0² of n₁ (b) var(X₁-X₂) = + 0² n₂

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Question
show that if X11, X12,..., X1, X21, X22,..., X2n₂ are
independent random variables, with the first n constitut-
ing a random sample from an infinite population with the
mean μ₁ and the variance of and the other n2 constitut-
ing a random sample from an infinite population with the
mean μ2 and the variance o2, then
1
M2
(a) E(X₁-X₂) = μ₁ −μ2;
07 0 22
(b) var(X₁-X₂) = +
n₁
n₂
Transcribed Image Text:show that if X11, X12,..., X1, X21, X22,..., X2n₂ are independent random variables, with the first n constitut- ing a random sample from an infinite population with the mean μ₁ and the variance of and the other n2 constitut- ing a random sample from an infinite population with the mean μ2 and the variance o2, then 1 M2 (a) E(X₁-X₂) = μ₁ −μ2; 07 0 22 (b) var(X₁-X₂) = + n₁ n₂
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