3. (a) Let X₁, X2,..., Xn be n mutually independent normal variables with means and variances ²,022,...2, respectively. Show that the linear function of Y = cX, is NECH, Eco) where C₁,C₂,..., C, are real constants. (b) Use the result above to compute P(X
3. (a) Let X₁, X2,..., Xn be n mutually independent normal variables with means and variances ²,022,...2, respectively. Show that the linear function of Y = cX, is NECH, Eco) where C₁,C₂,..., C, are real constants. (b) Use the result above to compute P(X
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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3.
Transcribed Image Text:3. (a) Let X₁, X2,..., Xn be n mutually independent normal variables with means e flyt
and variances o,²,2,..., respectively. Show that the linear function of Y = C,X, is
NECH, Eco) where C₁,C₂,...,,, are real constants.
(b) Use the result above to compute P(X<Y) where X and Y are independent random
variables with normal distributions N (4,9) and N (7,16), respectively.
(c) Let X and Y represent the means of random samples, each of a size 4, from the
respective normal distributions of (b). Compute P(X<Y). Compare this to the
for P(X<Y) found in (b).
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