Homework SourseGiven 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
Given E (X + 4) = 10 and E [(X + 4)2] = 116.
a) Var(X + 4) = E [(X + 4)2] - {E (X +4)}2
=116 - (10)2
= 116 - 100
= 16
b) µ = E(X) ,
Since E(X + 4) = 10
E(X) + 4 = 10
==>E(X) = 10 - 4 = 6
c) s2 = Var(X)
Var(X + 4) = Var(X) (Since varianceis independent of change of origin)
? s2 = Var(X) =16
![Given E(X + 4) = 10 and E[(X + 4)2] = 116, determine (a) Var(X + 4), (b) = E(X), and (c) 2 = Var(X ).SolutionGiven E (X + 4) = 10 and E [(X + 4)2] = 116. a) Var](/WebImages/30/given-ex-4-10-and-ex-42-116-determine-a-varx-4-b-ex-an-1083750-1761569523-0.webp "Given E(X + 4) = 10 and E[(X + 4)2] = 116, determine (a) Var(X + 4), (b) = E(X), and (c) 2 = Var(X ).SolutionGiven E (X + 4) = 10 and E [(X + 4)2] = 116. a) Var")
