Determine whether each of the following is true or false (note: the statement is

Question

Determine whether each of the following is true or false (note: the statement is true if it is always true, otherwise it is false). If you say it is true then refer to a known result or give a proof, while if you say it is false then give a counterexample, i.e., a particular case where it fails. (d) Let X be a random variable and Y = g (X) . Then J o yfy (y) dy Jo g (x) fx (x) dx (e) Let X be a random variable and a and b be constants. Then EaX +b] = aE [X] +b. (f) Let X be a random variable and a and b be constants. Then Var [aX + -a2 Var(X] (g) Let X be a random variable. Then Var [X 0 if and only if X 0.

Explanation / Answer

d)Correct Answer: True

e) Correct Answer: True

f) Correct Answer:  True

g) Correct Answer: True

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