In: Statistics and Probability
The number of coins that Jake spots when walking to work can be modeled as a Poisson process with unit rate of 3/half an hour. Suppose it takes Jake half an hour each day to walk to work, and half an hour to walk back. Each coin is equally likely to be a penny, a nickel, a dime, or a quarter. Jake ignores the pennies but picks up the other coins.
(a) Find the expected amount of money that Jake picks up on his way to work. (b) Find the variance of the amount of money that Jake picks up on a given day. (c) Find the probability that Josh picks up exactly 5 cents on his way to work. You do not have to calculate this. Just provide an expression.