Question

1. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3 then Var(4X-
2Y+6) is
d)256
4C9 - 20) +
c) 156
a) 9
b) 81​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Let X and Y be two independent random variables with Var(X) = 9 and Var(Y) = 3 then Var(4X- 2Y + 6)

a) 9

b) 81

c) 156

d)256

FORMULA TO BE IMPLEMENTED

We are aware of the formula on variance that

$\sf{Var(aX + bY + c) = {a}^{2}Var(X) + {b}^{2} Var(Y)}$

EVALUATION

Here it is given that Var(X) = 9 and Var(Y) = 3

Now

$\sf{Var(4X - 2Y + 6) }$

$\sf{= {4}^{2}Var(X) + {( - 2)}^{2} Var(Y)}$

$\sf{= 16Var(X) + 4 Var(Y)}$

$\sf{= (16 \times 9)+ (4 \times 3)}$

$\sf{=144 + 12}$

$\sf{= 156}$

FINAL ANSWER

Hence the correct option is c) 156

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Answer 2

Step-by-step explanation:

156

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