1. A committee consisting of 3 people is drawn randomly from a room which contains 25 males and 15 females. Let X be the number of females on the committee. So X has range 0, 1, 2, and 3. Find the distribution of X (use a tree diagram). Find the mean of X. Find the variance of X.
2. Let X have a uniform distribution on the interval (5,10). Find the probability that X is between 6 and 8. Obtain a random sample of size 15 from this distribution.
3. A real number X is drawn at random from the interval (0,1). A rectangle is formed with sides X and (1-X). Denote the area by Y = X*(1-X).
(a). Write an R function that returns a sample of size n on Y. Print out a sample of size 20.
(b). Estimate the expected value (mean) of Y based on a sample of size 10,000.