Solution Found!
Solved: Show that the following function satisfies the
Chapter 5, Problem 3E(choose chapter or problem)
Show that the following function satisfies the properties of a joint probability mass function.
Determine the following:
(a) \(P(X<0.5, Y<1.5)\) (b) \(P(X<0.5)\)
(c) \(P(Y<1.5)\) (d) \(P(X>0.5, Y<4.5)\)
(e) \(E(X), E(Y), V(X)\), and \(V(Y)\)
(f) Marginal probability distribution of X
(g) Conditional probability distribution of Y given that X = 1
(h) Conditional probability distribution of X given that Y = 1
(i) E(X | y = 1)
(j) Are X and Y independent?
Equation transcription:
Text transcription:
Text transcription:
P(X<0.5, Y<1.5)
P(X<0.5)
P(Y<1.5)
P(X>0.5, Y<4.5)
E(X), E(Y), V(X)
V(Y)
Questions & Answers
QUESTION:
Show that the following function satisfies the properties of a joint probability mass function.
Determine the following:
(a) \(P(X<0.5, Y<1.5)\) (b) \(P(X<0.5)\)
(c) \(P(Y<1.5)\) (d) \(P(X>0.5, Y<4.5)\)
(e) \(E(X), E(Y), V(X)\), and \(V(Y)\)
(f) Marginal probability distribution of X
(g) Conditional probability distribution of Y given that X = 1
(h) Conditional probability distribution of X given that Y = 1
(i) E(X | y = 1)
(j) Are X and Y independent?
Equation transcription:
Text transcription:
Text transcription:
P(X<0.5, Y<1.5)
P(X<0.5)
P(Y<1.5)
P(X>0.5, Y<4.5)
E(X), E(Y), V(X)
V(Y)
ANSWER:Solution 3E
Step1 of 11:
From the given problem we have:
x |
y |
|
-1 |
-2 |
1/8 |
-0.5 |
-1 |
1/4 |
0.5 |
1 |
1/2 |
1 |
2 |
1/8 |
Here our goal is:
a). We need to find
b). We need to find
c). We need to find
d). We need to find
e). We need to find
f). We need to find marginal probability distribution X.
g). We need to find conditional probability distribution of Y given that X = 1.
h). We need to find conditional probability distribution of X given that Y = 1.
i). We need to find
j). We need to check whether X and Y independent or not.
Step2 of 11:
a).
Suppose X and Y are discrete random variables then, The joint probability mass function must be satisfied,