MadeEasy Test Series: Probability - Expectation

Question

Suppose X and Y are random variables such that
E(X) = 1, Var (X) = 1, E(Y) = 2, Var (Y) = 2, Cov (X, Y) = 1
By using above values the following expressions are evaluated
(i) E(X + 2Y) = p

(ii) E(XY ) = q
(iii) Var(X – 2Y + 1) = r
The value of pq + r is ___________.

What is the formulae for point (iii) ?

Comments

The answer is 20. I have already taken this test :P

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My approach to (ii) point.From the above formula i mentioned i solved like

Var(X – 2Y + 1) = $ 1^2*V(X) + (-2)^2*V(Y) -2ab(COV(a,b)) $

=$ 1*1 + 4*2 -2*(1)(-2)(1) $

=$1+8+4$

=13

P.S:- Here i have taken b as -ve .Why is that incorrect as per image as shared?

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Got my mistake. Thank you!!!:)