# 1. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3 then Var(4X-2Y+6) isd)256 December 25, 2021 By Iris

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​

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

$$\sf{Var(4X – 2Y + 6) }$$

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

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

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

$$\sf{=144 + 12}$$

$$\sf{= 156}$$

Hence the correct option is c) 156

━━━━━━━━━━━━━━━━

1. Generally, what is the range of coefficient of skewness for data where the mode is ill-defined?(A) 0 to 1 (B) -1 to +1

https://brainly.in/question/26142979

2. if arithmetic mean of a seties is 45 and median is 40 then calculate the value of mode of that series

https://brainly.in/question/31548199