1. (Computer Experiment.) Suppose a coin has probability p of falling heads up. If we ?ip the coin many times, we would expect the proportion of heads to be near p. We will make this formal later. Take p = .3 and n = 1, 000 and simulate n coin ?ips. Plot the proportion of heads as a function of n. Repeat for p = .03.
2. (Computer Experiment.) Suppose we ?ip a coin n times and let p denote the probability of heads. Let X be the number of heads. We call X a binomial random variable, which is discussed in the next chapter. Intuition suggests that X will be close to n p. To see if this is true, we can repeat this experiment many times and average theX values. Carry out a simulation and compare the average of the X's to n p. Try this for p = .3 and n = 10, n = 100, and n = 1, 000.