If Y is a continuous random variable such that E[(Y − a) 2 ] < [infinity] for all a, show that E[(Y − a) 2 ] is minimized when a = E[Y ]. Hint: E[(Y − a) 2 ] = E[((Y − E[Y ]) + (E[Y ] − a))2 ]

Suppose a store sells an average of 80 cases of soda per day. assume that each case contains 24 cans of soda and that the store is open 10 hours per day. find the average number of soda that the store sells per hour.