Sum of random variables

9. (Sum of random variables, 12 points) Let X and Y be two negatively correlated random variables,

and X + Y be their sum. Select all of the correct statements from below. (Note: keep in mind that

incorrect selections will be graded with negative points.)

Corr (X,X) < 0

Corr (X,X) = 0

Corr (X,X) > 0

Cov [Y, Y ] < Var [Y ]

Cov [Y, Y ] = Var [Y ]

Cov [Y, Y ] > Var [Y ]

Cov [X, Y ] < 0

Cov [X, Y ] = 0

Cov [X, Y ] > 0

E[X + Y ] < E[X] + E[Y ]

E[X + Y ] = E [X] + E[Y ]

E[X + Y ] > E[X] + E[Y ]

Var [X + Y ] < Var [X] + Var [Y ]

Var [X + Y ] = Var [X] + Var [Y ]

Var [X + Y ] > Var [X] + Var [Y ]

The standard deviation of X + Y is smaller than the sum of the standard deviation of X and

the standard deviation of Y

The standard deviation of X + Y is equal to the sum of the standard deviation of X and the

standard deviation of Y

The Standard deviation of X + Y is larger than the sum of the standard deviation of X and

the standard deviation of Y

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