Question

1. If the joint probability distribution of X and Y is given by f(x, y) for = 1,2,3; y=0,1,2,3 · 42

Answer 1

a)

marginal distribution of X: f(x)=
Σ f(x, y) y=0
   =
+y)/42 у:0
=(4x+6)/42=(2x+3)/21   for x=1,2,3

b)

marginal distribution of Y: f(y)=
3 Σ f(x, y)
   =
Σ (z + y)/42 r=1
=(6+3y)/42=(y+2)/14 for y=0,1,2,3

3 a)

E(XY)= =(0*1*(0+1)/42+0*2*(0+2)/42+...+3*3*(3+3)/42) =4.000

〉 〉-.ry(x + y)/42 r=1 y=0

b)

E(X)=$sum_{x=1}^{3}x(2x+3)/21$ =1*(2*1+3)/21+2*(2*2+3)/21+3*(2*3+3)/21 =46/21

c)E(Y)= =1*(1+2)/14+2*(2+2)/14+3*(3+2)/14=13/7

Σ y(y +2)/14 y=0

d)

Cov(X,Y)=E(XY)-E(X)*E(Y)=-0.068