4.45. (Class Exercise) For a single toss of a coin, let y = 1 for a head and y = 0 for a tail. This simulates the vote in an election with two equally-preferred candidates.

(a) Construct the probability distribution for y, and find its mean.

(b) The coin is flipped ten times, yielding six heads and four tails. Construct the sample data distribution.

(c) Each student in the class should flip a coin 10 times and calculate the proportion of heads in the sample. Summarize the empirical sampling distribution by plotting the proportions for all students. Describe the shape and spread of the sampling distribution compared to the distributions in

(a) and (b).

(d) If we performed the experiment of flipping the coin 10 times a very large number of times, what would we get for the (i) mean and

(ii) standard deviation of the sample proportion values? You can use 0.50 as the standard deviation of the distribution in (a).