73. Given two independent random samples, X₁, X2, ..., Xm from N(μx, oz) and Y₁, Y2, ..., Yn from N(μy, o), how are the following functions of this sample distributed? You may assume m 1 X = ΣΧ., Sk m i=1 (a) X-Y = 1 m-1 m Σ(x − x), Y = i=1 1 n n i=1 Y and s = 1 n-1 n Σ(Yi-Y)² i=1
73. Given two independent random samples, X₁, X2, ..., Xm from N(μx, oz) and Y₁, Y2, ..., Yn from N(μy, o), how are the following functions of this sample distributed? You may assume m 1 X = ΣΧ., Sk m i=1 (a) X-Y = 1 m-1 m Σ(x − x), Y = i=1 1 n n i=1 Y and s = 1 n-1 n Σ(Yi-Y)² i=1
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:73. Given two independent random samples, X₁, X2,..., Xm from N(μx, oz) and Y₁, Y2, ..., Yn from N(μy, o),
how are the following functions of this sample distributed? You may assume
X =
O
==
(a) X-Y
(b)
m
m
ΣX₁, sx
i=1
(X-Y)-(HX-HY)
=
m
4 Eur
1
m-1
i=1
1
-Σ(X₁-X)², Y ==
n
n
i=1
Y and s
-
1
n-1
12
-Σ(Yi-Y)²
i=1
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