Exercise 1. Customers at a coffee shop ask for hot, denote it X, = 0, or cold, denote it X, = 1, beverages according to a Bernoulli process with

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Exercise 1. Customers at a coffee shop ask for hot, denote it X, = 0, or cold, denote it X, = 1,beverages according to a Bernoulli process with parameter p. Let N denote the first time that acustomer wants the same kind as their predecessor.(1) Find the PMF of N.(2) What is the probability that XN+1 = 1?(3) Cold drinks take 30 seconds to prepare and hot drinks take 60 seconds. What is the expectedtime taken to serve the first one hundred customers?(4)The shop only has enough ice for m cold beverages. What is the expected total number ofcustomers served when the supply is exhausted?(5) What is the probability that no hot drinks have been requested at ( or before) the moment theice is exhausted?