Answer:
0.4696
Step-by-step explanation:
Step 1: we say,
p(0,1) + p(0,2) + p(1,1) + p(1,0) + 3p(1,2) + p(0,0) = 1
P(Y=0) + p(X=0) - p(X=0, Y=0) + 4p(1,1) = 1.
Step2: let p(1,1)= w.
Therefore, 3w= p(1,2)
E(XY)= 2p(1,2) + p(1,1)
= 7w.
E[(XY)^2] = 4p(1,2) + p(1,1)
=13w.
variance(XY) = E[(XY)^2] - [E( XY)]^2
= -49w+ 13w
therefore, 0,1 are elements of w.
Step 3: calculate the derivative
13= 2x × 49
X = 13÷98
X= 0.1326
X=0, Y=0 = 1
= 1 - [0.1326 × (-4)]
= 0.4696.
