Practice question · Select all that apply
Select every statement that is true for all random variables X and Y.
Hints
- Ask which rules need an independence assumption and which do not.
- Variance measures spread, so shifting every value by the same amount changes nothing.
Show the answer
- A. E[2X + 5] = 2 E[X] + 5
- B. E[X + Y] = E[X] + E[Y]
- E. Var(X + 5) = Var(X)
Why
Expectation is linear unconditionally, and shifting a variable by a constant slides the whole distribution without altering its spread. Variances add only for independent variables, and variance is an average of squares, so it can never be negative.
Practise Random Variables and Distributions
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