Consider the following joint distribution of X and Y X\Y -4 2 7 Sum 1/4 1/8 1/8 1/8 1/8 1/4 1/2 Sum 3/8 3/8 1/4 1 Find: 1. E(X) 2. E(Y) 3. ÇoylXY) 4. Ox, Oy 5. ρ(Χ, Υ)
Consider the following joint distribution of X and Y X\Y -4 2 7 Sum 1/4 1/8 1/8 1/8 1/8 1/4 1/2 Sum 3/8 3/8 1/4 1 Find: 1. E(X) 2. E(Y) 3. ÇoylXY) 4. Ox, Oy 5. ρ(Χ, Υ)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Consider the following joint distribution of X and Y
X\Y
-4
2
7
Sum
1/8
1/4
1/4
1/8
1/8
1/4
1
5
1/8
1/2
Sum
3/8
3/8
1
Find:
1. Е(X)
2. E(Y)
3. ÇoylXY
4. Ох, бу
5. p(X,Y)
Transcribed Image Text:A probability distribution for two (or more) random variables is shown as a
joint probability distribution.
The standard is to utilize X and Y instead of A and B for events.
f(x,y) = P(X= x, Y = y) is the formal definition.
The joint distribution's entire purpose is to find a link between two
variables.
Step 2: Solution
Part 1)
E(X) = Ex. P(x)
= (1) (}) + (5) ()
=3
Part 2)
E(Y) = Ey. P(y)
= (-4) () + (2) (}) +7(†)
= 1
Part 3)
ΣΧ. Υ.Pxy (Χ, Υ)
= (1)(-4) (4) + (1) (2) (4) + (1) (7) (→) + (5) (-4) (4)
+ (5) (2) () + (5) (7) (G)
E (XY) =
= 1.5
COV (х,у) %3D Е (ХҮ) —
Ε (X) E (Υ)
= 1.5 - (3) (1)
= -1.5
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