1. Each day Max commutes to N 1' U on his bike, but it the weather is bad, he takes the subway. The subway costs $2.75 per ride, so on days he takes the subway he spends $5.50. Over the course of a semester, Max commutes to NYU 75 times. Each day there is 20% chance of bad weather that would prevent Max from taking his bike. Every day the weather is completely independent. of the previous day. (a) How much is he expected to spend on subway fares in a semester? (b) What is the variance of the amount of money he spends on the subway (Hint: variance of a binomial r.v. is np p}) (c) Using R, nd the probability he takes the subways between 8 and 22 times. Below is an example of nding the probability he takes it between 14 and 17 times: > pbinom(q = 17, size = 75, prob = .2) - pbinom(q = 13, size = 75, p: [1] 0.4275844