P(X < 0.5, Y < 1.5 ) =
P(X ≤ 1) =
P(X < 1.5) =
P(X > 0.5, Y < 1.5 ) =
E(X) =
V(X) =
E(Y) =
V(Y)=
Possible Values of X : 0,1,2
Possible value of Y : 0,1,2
P(X<0.5, Y<1.5) = P(0,0) + P(0,1) = 1/4+1/8 = 3/8
P(X 1) = P(X=0,Y=0)+P(X=0.Y=1)+P(X=1,Y=0)+P(X=1,Y=1) = 1/4+1/8+1/8+1/4=3/4
also, P(X 1) = 1-P(X>1) = 1-P(X=2,Y=2) = 1-1/4 =3/4
P(X 1) = 3/4
P(X>0.5, Y<1.5) = P(1,0)+P(1,1)=1/8+1/4=3/8
PX(X=0) = P(X=0,Y=0)+P(X=0,Y=1) = 1/4+1/8 =3/8
PX(X=1) = P(X=1,Y=0)+P(X=1,Y=1) = 1/8+1/4 =3/8
PX(X=2) = P(X=2,Y=2) = 1/4
E(X) =7/8
V(X) = 39/64
PY(Y=0) = P(X=0,Y=0)+P(X=1,Y=0) = 1/4+1/8 =3/8
PY(Y=1) = P(X=0,Y=1)+P(X=1,Y=1) = 1/8+1/4 =3/8
PY(Y=2) = P(X=2,Y=2) = 1/4
E(Y) = 7/8
V(Y) = 39/64
P(X < 0.5, Y < 1.5 ) = P(X ≤ 1) = P(X < 1.5) = P(X > 0.5, Y < 1.5 ) = E(X) = V(X) = E(Y) = The following is a joint probability mass function. x xx (x,) 1/4 0 1 1/8 10 1/8 1 1 1/4 2 2 1/4 Determine the following. Give exact answers in form of fraction.
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