1) Every time you go to a beach for vacation, you take home a little sand to keep as a souvenir. Over your lifetime, you have done this exactly 100 times. On each visit the weight of sand you take home (measured in ounces), varies, but follows a U(10-sqt(48)/2, 10+sqt(48)/2) distribution. Assuming the amounts you take home on each trip are independent, estimate the probability that you have collected at least 980, but no more than 1030 ounces of sand.
2) You have a list of chores to do at home, but are expecting family to arrive shortyly. The amount of tie until their arrival (measured in hours) can be modeled as an Exp(2) random variable. Your list of chores contains 4 activities each of which take 15 minutes to complete. Let X be the (whole) number of chore you complete before your family arrives. Find the CDF of X.
3) Let X and Y be independent random variables with X~U(0,12) and Y~Exp(1). What is Cov(X,Y)?