1.Consider the following joint probability density function (pdf) of the random variables X and Y:

f(x,y)=0< x < 8,0 < y < 9

=0elsewhere

(a) Calculate the constant k if P(4 < X < 7, k < Y < 6) = 0,20(11)

(b) Are the random variables X and Y independent? Show.(8)

(c) Calculate the correlation coefficient between X and Y.(20)

2.X₁ and X₂ are random variables with ₁ = 20, ₂ = 16, ₁ = 6, ₂ = 9 and (X₁, X₂) = 0,28.

Calculate

( a )E(M) ifM = 5X₁X₂+3X₁²(7)

( b )var( X₁ + X₂)(4)