Picture bread that is sliced with thickness Xi that is uniform in a given slice i, but varies from slice to slice.
a. The usual way to construct a sandwich is with two slices of bread, but it can also be constructed by folding over a single slice of bread. Which of the random variables 2X1 and X1 + X2 represents the thickness of bread for a sandwich constructed from two individual slices, and which represents the thickness of bread for a sandwich constructed by folding a single slice?
b. If two slices are randomly selected for constructing a sandwich, and one of the slices is on the thin side, the other slice may be thick, so that the sandwich itself is not unusually thin. If one slice is randomly selected, and it is on the thin side, then the folded-over part must also be thin. In which case is there more of a tendency for extremely thin or thick sandwiches-when a sandwich is constructed from two independent slices, or when it is constructed by folding over a single slice?
c. Suppose thickness Xi of any randomly chosen slice has mean 0.5 inches. Find the mean of 2X1 and find the mean of X1 + X2. Are they equal? If not, tell which is larger and why.
d. Suppose thickness Xi of any randomly chosen slice has standard deviation 0.01 inches. Find the standard deviation of 2X1 and find the standard deviation of X1 + X2. Are they equal? If not, tell which is larger and why.