A fair tetrahedral die, with its faces labelled zero (U), one twice. The score on each throw is the number shown on the face which lands on the floor. Random variables X and Y are defined as follows: X is the remainder when the SUM of the scores is divided by FOUR. Y is the remainder when the PRODUCT of the scores is divided by THREE. (a) Show that the joint probability mass function p(x,y) for X and Y, is that which is given below. p(x,y) 3/16 1 1/16 1 4/16 2 3/16 1 1/16 3. 2/16 3. 2/16 (b) Determine each of the marginal probability mass functions f1 (x) and f2 (y). (c) Determine each of the probabilities p(X = 0|Y = 1) and p(X = 0|Y > 0). (d) Determine E (X), Var (X), E(Y),Var (Y), and p x.r. %3D %3! %3D
A fair tetrahedral die, with its faces labelled zero (U), one twice. The score on each throw is the number shown on the face which lands on the floor. Random variables X and Y are defined as follows: X is the remainder when the SUM of the scores is divided by FOUR. Y is the remainder when the PRODUCT of the scores is divided by THREE. (a) Show that the joint probability mass function p(x,y) for X and Y, is that which is given below. p(x,y) 3/16 1 1/16 1 4/16 2 3/16 1 1/16 3. 2/16 3. 2/16 (b) Determine each of the marginal probability mass functions f1 (x) and f2 (y). (c) Determine each of the probabilities p(X = 0|Y = 1) and p(X = 0|Y > 0). (d) Determine E (X), Var (X), E(Y),Var (Y), and p x.r. %3D %3! %3D
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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