Given EX 4 10 and EX 42 116 determine a VarX 4 b EX an

Given E(X + 4) = 10 and E[(X + 4)²] = 116, determine (a) Var(X + 4), (b) = E(X), and (c) ² = Var(X).

Solution

a)

Var(x + 4) = E[(x+4)^2] - E[x+4]^2 = 116 - 10^2 = 16 [answer]

b)

As E(x + c) = E(x) + c,

u = E(x) = E(x+4) - 4 = 10 - 4 = 6 [answer]

c)

As var(x+c) = var(x),

var(x) = var(x + 4) = 16 [answer]