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
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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:A fair tetrahedral die, with its faces labelled zero (0), one (1), two (2), and three (3), is thrown
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
0.
1/16
1
0.
4/16
3/16
1
1/16
3
0.
2/16
3.
2/16
(b) Determine each of the marginal probability mass functionsfi(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
%3D
%3D
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