Question

You roll three dice, and you define the random variable `X` as the number of heads obtained. What are all possible values of the random variable `X`?

Answer 1

I believe you mean either 'you flip a coin three times' or 'you flip three coins'.

X is called a 'random variable' because before we flip the coins we don't know how many heads we are going to get. But we can say something about all the possible values for X.

Since each flip of a coin is independent from other flips, the possible value of the random variable X are {0, 1, 2, 3}, i.e. you could get 0 heads or 1 head or 2 heads or 3 heads.

Try another one where you think about four tosses of a die. Let random variable Y denote the number of 6s in four tosses of a die. What are all the possible values of random variable Y?