1. Let X and Y be two independent random variables with Var(X)=9 and Var(Y)=3 then Var(4X-2Y+6) isd)2564C9 – 20) +c) 156a) 9b) 81 About the author Iris
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 [tex] \sf{Var(aX + bY + c) = {a}^{2}Var(X) + {b}^{2} Var(Y)}[/tex] EVALUATION Here it is given that Var(X) = 9 and Var(Y) = 3 Now [tex] \sf{Var(4X – 2Y + 6) }[/tex] [tex] \sf{= {4}^{2}Var(X) + {( – 2)}^{2} Var(Y)}[/tex] [tex] \sf{= 16Var(X) + 4 Var(Y)}[/tex] [tex] \sf{= (16 \times 9)+ (4 \times 3)}[/tex] [tex] \sf{=144 + 12}[/tex] [tex] \sf{= 156}[/tex] FINAL ANSWER Hence the correct option is c) 156 ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 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 Reply
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
[tex] \sf{Var(aX + bY + c) = {a}^{2}Var(X) + {b}^{2} Var(Y)}[/tex]
EVALUATION
Here it is given that Var(X) = 9 and Var(Y) = 3
Now
[tex] \sf{Var(4X – 2Y + 6) }[/tex]
[tex] \sf{= {4}^{2}Var(X) + {( – 2)}^{2} Var(Y)}[/tex]
[tex] \sf{= 16Var(X) + 4 Var(Y)}[/tex]
[tex] \sf{= (16 \times 9)+ (4 \times 3)}[/tex]
[tex] \sf{=144 + 12}[/tex]
[tex] \sf{= 156}[/tex]
FINAL ANSWER
Hence the correct option is c) 156
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Learn more from Brainly :-
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
Step-by-step explanation:
156
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