Consider an urn with three red cubes, four blue cubes and two yellow cubes. Three cubes are drawn uniformly at random from the urn; let X be the number of red, Y be the number of blue, and Z be the number of yellow cubes drawn. (a) Determine the expectation of X. (b) Determine the variance of Y. (c) Determine the correlation of X + Y and Z.
Consider an urn with three red cubes, four blue cubes and two yellow cubes. Three cubes are drawn uniformly at random from the urn; let X be the number of red, Y be the number of blue, and Z be the number of yellow cubes drawn. (a) Determine the expectation of X. (b) Determine the variance of Y. (c) Determine the correlation of X + Y and Z.
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:2. Consider an urn with three red cubes, four blue cubes and two yellow cubes. Three
cubes are drawn uniformly at random from the urn; let X be the number of red, Y be
the number of blue, and Z be the number of yellow cubes drawn.
(a) Determine the expectation of X.
(b) Determine the variance of Y.
(c)
Determine the correlation of X +Y and Z.
(Hint: you don't need to calculate any sums for any part of this question!)
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