11. Correct. The answer is true

(a) E(U) = ∑ uf ( u, v )

u v

E(U) = ∑ [∑ uf ( u, v )]

u v

E(U) = 0*6b + 1*14b + 2*22b

E(U) = 58b

E(U) = 29/21

(b) E(V) = ∑ vf ( u, v )

u v

E(V) = ∑ v[∑ f ( u, v )]

u v

E(V) = 0*6b + 1*9b + 2*12b + 3*15b

E(V) = 78b

E(V) = 13/7

(c) E(UV) = ∑ uvf ( u, v )

u v

E(UV) =0*0*0+0*1*b+0*2*2b+0*3*3b+1*0*2b+1*1*3b+1*2*4b

+1*3*5b+2*0*4b +2*1*5b+ 2*2*6b+2*3*7b

E(UV) =102b

E(UV) =17/7

(d) E(U2) = ∑ u2f ( u, v )

u v

E(U2) = ∑ u2 [∑ f ( u, v )]

u v

E(U2) = 02*6b+12*14b+22*22b

E(U2) = 102b

E(U2) = 17/7

 

(e) E(V2) = ∑ v2f ( u, v )

u v

E(V2) = ∑ v2 [∑ f ( u, v )]

 u v

E(V2) = 02*6b+12*9b+22*12b+32*15b

E(V2) =192b

E(V2) =32/7

(f) su2 = E(U2)-[E((U)]2

su2= 17/7-(29/21)2

su2=230/441

(g) sv2 = E(V2)-[E((V)]2

sv2= 132/7-(13/7)2

sv2 =55/49

(h) sUV= E(UV) - E(U)E(V)

sUV=17/7 - (29/21)(13/7)

sUV= -20/147

(i) r = sUV/(sUsV)

r = (-20/147)/ √((230/441)(55/49))

r = -20/√(230)*√(55)

r = - 0.2103