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