A four-sided (tetrahedral) die has a different number 1, 2, 3 or 4 affixed to each face. Or y given roll, each of the four numbers is equally likely to occur (face down). An experiment sists of rolling the die twice and recording the two values obtained in order. Random variable represents the lesser of the two values, random variable Y represents the first value minus e second.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter0: Preparing For Algebra
Section0.11: Simple Probability And Odds
Problem 13E
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8 A four-sided (tetrahedral) die has a different number 1, 2, 3 or 4 affixed to each face. On
any given roll, each of the four numbers is equally likely to occur (face down). An experiment
consists of rolling the die twice and recording the two values obtained in order. Random variable
X represents the lesser of the two values, random variable Y represents the first value minus
the second.
(a) Construct the sample space for the experiment.
(b) Construct the induced sample space for (X, Y).
(c) Construct the probability distributions for X and Y.
(d) Obtain ux, µY, 0X, 0y and Cov(X, Y) = oxy.
Transcribed Image Text:8 A four-sided (tetrahedral) die has a different number 1, 2, 3 or 4 affixed to each face. On any given roll, each of the four numbers is equally likely to occur (face down). An experiment consists of rolling the die twice and recording the two values obtained in order. Random variable X represents the lesser of the two values, random variable Y represents the first value minus the second. (a) Construct the sample space for the experiment. (b) Construct the induced sample space for (X, Y). (c) Construct the probability distributions for X and Y. (d) Obtain ux, µY, 0X, 0y and Cov(X, Y) = oxy.
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