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Which of the following statement is true? A. For any discrete random variable X and constants a and b, E(aX+b) = (a + b). E(X) B. For any discrete random variable X and constants a and b, V(aX+b) = . C. If a constant c is added to each possible value of a discrete random variable X, then the variance of X will be shifted by that same constant amount. D. If a constant c is added to each possible value of a discrete random variable X, then the expected value of X will be shifted by that same constant amount.

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Answer:

A. False

B. False

C. False

D. True

Step-by-step explanation:

A. False

Remember that E[aX+b] = aE[X] + b, therefore the equality would be true only if E[X] = 1.

B. False

Remember that [tex]V[aX+b] = a^2 V[X][/tex].

C. False

In other words they are telling you in words that [tex]V[X+b] = V[X]+b[/tex], that is false because [tex]V[X+b] = V[X][/tex]

D. True

That is a property of the expected value E[X+b] = E[X]+b

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