Question

Suppose A B C be random variable with

E[A] = 3 and E [A^2]= 10

Var[B] = 5, E[C] = 2

E [c^2] = 7 we know A and B are independent

E[AC] = 5

Cov(B, C) = 2 please find Var[3A +B - C]

Answer 1

2 Var [ 3A + B-c] = 39. varCA) + var(B) varly + 2..cov (A,B) -2COVCA,C) 02€– 2 cou ( Bic) given - ECA) = 3, E(A3) = 10 , VOO(B)=5 E(C) = 299 € (c?) 1, E(AC) = 5 cov (Bo) = 2 & Now var (A) = E(AB) - [ECA)]? 10 2. varCA) 31 Var (c) = E (C?) -[ECC) 7. 4 - 3 9 her Var (c)

=O CONCA,C) ECAC). ELA) E (0) 5 (3 x 2) 5 6 Covca, t? -1 COUCA, B) CA&B are independent) Now, Var(3A +B-C) 3? x 1 + 5 + 3 + 2x(0) - 2*(-1) - 2 X (2) g + 5 + 3 +0+2 - 4 15 var (A + B-C) = 15 T
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