Suppose three unfair coins are tossed, a nickel, a dime, and a quarter. The probability of tossing a head on the nickel is 0.35; the probability of tossing a head on the dime is 0.20; and the probability of tossing a head on the quarter is 0.65. Let the random variable X be the number of heads observed on each toss of the three coins. So the range of X is the set and there are elements of the sample space.
(a) Find the probability function of X.
(b) Find the expected value of X:
(c) Find the variance and standard deviation of X.