Question: Roundoff errors. Suppose you balance your checkbook by rounding amounts to the nearest dollar. Between 0 and 49 cents, drop the cents: between 50 and 99 cents, drop the cents and add a dollar. Find approximately the probability that the accumulated error in 100 transactions is greater than 5 dollar (either way)
a) assuming the numbers of cents involved are independent and uniformly distributed between 0 and 99:
b) assuming each transaction is an exact dollar amount with probability 1/4 and given not an exact dollar amount the number of cents is uniformly distributed between 1 and 99, independently for different transactions.