The random variable X for number of heads in a single coin toss has possible values 0 and 1, each with probability 0.5.
a. Explain why 0.5 is the mean of X.
b. Each of the two values of X has a distance of 0.5 away from the mean. Find the weighted average of the two squared distances from the mean, weighting each with probability 0.5, and take the square root to find the standard deviation of X.
c. Explain why your answer to part (b) makes sense as a measure of the typical distance of values from their mean.