Question

how it is 90/70 please explain with formula

Ε(ay) - ΣΣ κ.ν.f(x,y) 18 36 6 18 12 70 70 70 70 70 90 90 1ος 14

Answer 1

The expected value of XY is computed as:

= Sum product of the X, Y and joint probabilities(X, Y)

From the given table, we see that:
P(X = 1, Y = 1) = 18/70  

Therefore the term for that cell would be given as: 1*1*(18/70) = 18/70

Similarly the terms are computed for each combination for X and Y in the given table. Therefore the expected value here is computed as:

E(XY) = XYP(X = 1, Y = y)

E(XY) = 1*1* P(X = Y = 1)+1*2* P(X = 2, Y = 1)+1*3* P(X = 3, Y = 1)+2*1*P(X = 1, Y = 2)+2*2P(X = Y = 2)+3*2P(X = 3, Y = 2)

E(XY) = 18 - 2* 18 70 70 3* 2 70 2*9 70 4*3 70 T T

18 36 6 E(XY) = 70 + 70 + 70 18 70 +

E(XY) = 30

This is the required expected value of XY here.