If X and Y are random variables, then the statement \"E[X + Y] = E[X] + E[Y]\" i

Question

If X and Y are random variables, then the statement "E[X + Y] = E[X] + E[Y]" is always true

True

False

Let X be a random variable and c be a constant. Then Var(cX) = c Var(X) is always true

True

False

When tossing a pair of fair dice, which pair of random variables are independent?

A.

X: the number of the first die

Y: the number of distinct values (Y=1 if two dice land on the same number; Y=2 if two dice land on different numbers)

B.

X: number of dice that land on 1

Y: sum of the two dice

C.

X: sum of the two dice

Y: difference between the two dice

Choose the best answer. If the correlation coefficient between two random variables X and Y is equal to 0.7, then when X is large and positive,

A.Y tends to be small and negative

B.Y tends to be large and negative

C.Y takes on its smallest possible value for sure

D.Y takes on its largest possible value for sure

E.Y tends to be large and positive

F.Y tends to be small and positive

If Cov[X,Y] = 0, then X and Y are independent

True

False

If X and Y are random variables, then the statement "E[X + Y] = E[X] + E[Y]" is always true

True

False

Let X be a random variable and c be a constant. Then Var(cX) = c Var(X) is always true

True

False

When tossing a pair of fair dice, which pair of random variables are independent?

A.

X: the number of the first die

Y: the number of distinct values (Y=1 if two dice land on the same number; Y=2 if two dice land on different numbers)

B.

X: number of dice that land on 1

Y: sum of the two dice

C.

X: sum of the two dice

Y: difference between the two dice

Choose the best answer. If the correlation coefficient between two random variables X and Y is equal to 0.7, then when X is large and positive,

A.Y tends to be small and negative

B.Y tends to be large and negative

C.Y takes on its smallest possible value for sure

D.Y takes on its largest possible value for sure

E.Y tends to be large and positive

F.Y tends to be small and positive

If Cov[X,Y] = 0, then X and Y are independent

True

False

Explanation / Answer

1 ) If X and Y are random variables, then the statement " E[X + Y] = E[X] + E[Y] " is always true .

------------------------------ TRUE .

2 ) Let X be a random variable and c be a constant. Then Var(cX) = c Var(X) is always true .

------------------------------- FALSE

3 ) When tossing a pair of fair dice, which pair of random variables are independent ?

B ) X: number of dice that land on 1

Y: sum of the two dice

4 )   If the correlation coefficient between two random variables X and Y is equal to 0.7, then when X is large and positive ,

F ) Y tends to be small and positive

5 ) If Cov[X,Y] = 0, then X and Y are independent .

------------------------ FALSE .

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