1. State the two conditions for probabilities for discrete random variables. 2. Suppose you toss a fair coin three times. Let the random variable X be the number of heads obtained. a) List the entire sample space (S). b) Construct the probability distribution table (or find the probability distribution of X). c) What is the probability that the number of heads is i) exactly 2 ii) at least 2 iii) at least one head d) Find the expected value of X e) Find the mean of X f) Find the variance of X g) Find the standard deviation of X