Question

For the joint PMF given below for random variables L and T, mark all answers that are correct. You may mark as many as needed. X=4 0.10 Pxy(x,y) Y=1 Y=2 Y=3 X=2 0.22 0.14 0.18 0.16 0.20 a. E[X] = 2.92 Ub. F[Y] = 1.28 c. E[x2] = 5.78 d. E[Y2] = 4.94 e Var[x] = 1.99 Var[Y] = 0.70 g. E[X|Y=2] = 3.07 E[Y|X=2] = 1.89 i. E[XY] = 6.40 C j. Cov[X.Y] = 0.24

Answer 1

	x
y	2	4	Total
1	0.22	0.1	0.32
2	0.14	0.16	0.30
3	0.18	0.2	0.38
Total	0.54	0.46	1.00

marginal distribution of y:
y	P(y)	yP(y)	y^2P(y)
1	0.320	0.320	0.320
2	0.300	0.600	1.200
3	0.380	1.140	3.420
total	1.000	2.060	4.940
E(y)	=		2.0600
E(y^2)	=		4.9400
Var(y)=	E(y^2)-(E(y))^2=		0.6964

marginal distribution of x:
x	P(x)	xP(x)	x^2P(x)
2	0.540	1.080	2.160
4	0.460	1.840	7.360
total	1.000	2.920	9.520
E(x)	=		2.9200
E(x^2)	=		9.5200
Var(x)=σy=	E(x^2)-(E(x))^2=		0.9936
standard deviation =σy =			0.9968

Covar(x,y)=E(XY)-E(X)*E(Y)=			0.14
Correlation coefficient ρ=Cov(X,Y)/√(σx*σy)=			0.1741

Correct options are:

a)E(X) =2.92

d)E(Y²)=4.94

f)Var(Y) =0.70

g)E(X|Y=2) =3.07