1.A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.

a What is the probability that an individual waits between 2 and 7 minutes?

b.What are the mean and variance values for waiting time at this bus stop

There are 15 different marbles and 3 jars. Suppose you are throwing the marbles in the jars and there is a 20%, 50% and 30% chance of landing a marble in jars 1, 2 and 3, respectively.

Note: Stating the distribution and parameters will give you 4 points out of the 7.

1. a. What is the probability of landing 4, 6 and 5 marbles in jars 1, 2 and 3 respectively?
2. b. Suppose that out of the 15 marbles 7 are red and 8 are blue. If we randomly select a sample of size 5, what is the probability that we will have 3 blue marbles?
3. c. Suppose we will throw marbles at the jars, until we have landed three (regardless of color) in jar 1. What is the probability that we will need to throw ten marbles to achieve this?