Give correct answer when have two random variables, X and Y. X is the value of a fair die, Y is the result of a coin flip, with heads being 1 and tails being 0.

That the expectation of XY is not multiplicative, i.e.: E[X]E[Y] is not necessarily equal to E[XY]. But I'm confused about what E[XY] means in the first place. That is, is E[XY] each possible value of the two events combined, multiplied by the probability that the two events occur?

That is, is

Due to a typo the last equation

That concerned with how to calculate E[XY] in the quickest way possible, but how to interpret what E[XY] means. E[X]E[Y]=E[XY] for independent events doesn't concern me as much as why that is the case, and how to manually evaluate E[XY] in order to prove that indeed E[XY]=E[X]E[Y].