Supposeastudenttakesthebustouniversityeveryday.Thereare3stopsalongtheway,andtheprobabilityofstoppingateachofthemis0.40,0.20and0.60,respectively.Assumeindependenceofstoppingateitherofthethreestops.Supposestoppingateachstopaddsexactly3,2,and4minutes,respectively,tothebustraveltime.Ifnostopshappen,thetimetouniversityis12minutes.

(a)Inhowmanywayscouldthebushavetostopenrouteandwhataretheprobabilitiesforeach?

(b) Write down the probability mass function of the commute time (in minutes) to UBC and compute its expected value and standard deviation.

(c) Let X be the random variable representing the number of stops made en route. Write down the probability mass function of X.

(d) Find the expected number of stops made en route. Interpret this value in the context of the question.