Quizzes: variance

Question: What is the variance of a fair six-sided die roll?
A) 2.5
B) 3.5
C) 2.9167
D) 1.5

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Answer: C) 2.9167

Question: If X is a random variable with variance Var(X) = 4, what is Var(2X)?
A) 4
B) 8
C) 16
D) 2

Answer: C) 16

Question: For a constant c, what is the variance of c?
A) 0
B) c
C) c/2
D) c^2

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Answer: A) 0

Question: A random variable Y has Var(Y) = 9. What is Var(3Y)?
A) 9
B) 18
C) 27
D) 81

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Answer: D) 81

Question: If X and Y are independent random variables, what is Var(X + Y)?
A) Var(X) + Var(Y)
B) Var(X) Var(Y)
C) Var(X) \cdot Var(Y)
D) Var(X + Y)

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Answer: A) Var(X) + Var(Y)

Question: If X is a random variable and c is a constant, what is Var(X + c)?
A) Var(X) + c
B) Var(X) + c^2
C) Var(X)
D) Var(X) + 2c

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Answer: C) Var(X)

Question: What is the variance of the sum of two independent random variables X and Y if Var(X) = 3 and Var(Y) = 4?
A) 1
B) 7
C) 12
D) 16

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Answer: B) 7

Question: What is the expected value of X^2 if X is a random variable with E(X) = 0 and variance Var(X) = 1?
A) 0
B) 1
C) 2
D) 3

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Answer: B) 1

explaination:

Var(X) = E(X^2)-(E(X))^2

Hence

E(X^2)=Var(X)+(E(X))^2=1+0=1


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