Construct the sampling distribution of the sample proportion of heads obtained in the experiment of flipping a balanced coin:
a. Once. (The possible sample proportion values are 0, if the flip is a tail, and 1, if the flip is a head. What are their probabilities?)
b. Twice. (The possible samples are {HH, HT, TH, TT}, so the possible sample proportion values are 0, 0.50, and 1.0, corresponding to 0, 1, or 2 heads. What are their probabilities?)
c. Three times. (There are 8 possible samples.)
d. Refer to parts a–c. Sketch the sampling distributions and describe how the shape is changing as the number of flips n increases.