91Ó°ÊÓ

Customers arrive at a bank at a Poisson rate \(\lambda\) Suppose that two customers arrived during the first hour. What is the probability that (a) both arrived during the first 20 minutes? (b) at least one arrived during the first 20 minutes?

Suppose that whether it rains tomorrow depends on past weather conditions only through the last 2 days. Specifically, suppose that if it has rained yesterday and today, then it will rain tomorrow with probability \(.8 ;\) if it rained yesterday but not today, then it will rain tomorrow with probability \(.3 ;\) if it rained today but not yesterday, then it will rain tomorrow with probability \(.4 ;\) and if it has not rained either yesterday or today, then it will rain tomorrow with probability. \(2 .\) What proportion of days does it rain?