The number of wrongly dialed phone calls you receive can be modeled as a Poisson process with the rate of one per month. For simplicity, assume there are four weeks in one month. a. Find the probability that it will take between two and three weeks to get the first wrongly dialed phone call.
b. Suppose that you have not received a wrongly dialed phone call for two weeks. Find the expected value and variance of the additional time until the next wrongly dialed phone call.