A student claims that for any random variable XXX, E[2X]=2E[X]E[2X] = 2E[X]E[2X]=2E[X]. Is this claim true?
Yes, this is the linearity of expectation.
No, it should be E[2X]=4E[X]E[2X] = 4E[X]E[2X]=4E[X].
No, it should be E[2X]=E[X]+2E[2X] = E[X] + 2E[2X]=E[X]+2.
Yes, but only if XXX is continuous.