I have a few exam review questions that I don't know how to solve. Maybe someone has a solution to it?
A lottery chooses a winning number x in the set S = {0, 1, 2, 3, ..., 999}
If you want to play, you pay $1 and choose a number y in S.
If y=x, then you receive \$700. So your net dollars is \$699. Otherwise, you lose $1.
Assume that you play this game once a day for one year (365 days)
each day, the lottery chooses a new winning number
each day, you choose a random y uniformly at random from the set S, independently from previous choices.
Define the random variable X to be the total amount of dollars that John wins during one year. Determine the expected value E(x).
It also gives you a hint: use linearity of expectation.