Question

The bivariate distribution of X and Y is described below: X Y 1 2 1 0.21 0.47 2 0.14 0.18 A. Find the marginal probability distribution of X. 1: .35 2: .65 B. Find the marginal probability distribution of Y. 1: .68 2: .32 C. Compute the mean and variance of X. Mean = .35+1.3 Variance = (.35+2.6)-(.35+1.3)^2 C. Compute the mean and variance of Y.

Answer 1

Answer:

Step-by-step explanation:

Given that the bivariate distribution of X and Y is described below:

x 1 2  

y    

1 0.21 0.14 0.35

0 0.47 0.18 0.65

Pdf of Y is

Y     1     0

p    0.68  0.32

C) Pdf of X is

x      1       2

p  0.35  0.65

Mean of X = $1(0.35)+2(0.65)=1.65$

Var(x) = E(x^2)-Mean ^2 = $1(0.35)+4(0.65)-1.65^2\\=2.95-2.7225\\=0.2275$

C) Mean of Y = 1(0.68)+0 = 0.68

Var(y) = 1(0.68)-0.68^2

= 0.2176