Question

The random variable X and Y have the following joint probability mass function: P(x,y) 23 0.2 0.1 0.03 0.1 0.27 0 4 0.05 0.15 0.1 a) Determine the marginal pmf for X and Y. b) Find P(X - Y> 2). c) Find P(X S3|Y20) e Determine E(X) and E(Y). f)Are X and Y independent?

Answer 1

Ans:

a)

Marginal pmf for X and Y:

x	2	3	4
P(x)=	0.37	0.33	0.3

y	-1	0	1
P(y)=	0.35	0.52	0.13

b)

P(X-Y>2)=0.1+0.2+0.05+0.1+0.15+0.1=0.7

c)P(X<=3/Y>=0)=0.27+0.1+0+0.03=0.40

d)

E(XY)=-1*2*0.1-1*3*0.2-1*4*0.05+0*2*0.27+0*3*0.1+0*4*0.15+1*2*0+1*3*0.03+1*4*0.1=-0.51

e)

E(X)=2*0.37+3*0.33+4*0.3=2.93

E(Y)=-1*0.35+0*0.52+1*0.13=-0.22

f)

Cov(X,Y)=E(XY)-E(X)*E(Y)=-0.51-2.93(-*0.22)=0.1346

As,Cov(X,Y) is not zero,so,X and Y are not independent.