A subway has good service 70% of the time and runs less frequently 30% of the time because of signal problems. When there are signal problems, the amount of time in minutes that you have to wait at the platform is described by the following probability density function and cumulative density function probability density function with signal problems = PT|SP(t) = .1e The cumulative distribution function is: -.1t rt FT|SP (t) = .le -.1t dt = 1 e.1t But when there is good service, the amount of time you have to wait at the platform is described by the following pdf and cdf: probability density function with good service = PT|Good(t) = .3e.t Fr|Good (t) = [" .3e -.3t dt = 1 e.t You arrive at the subway platform and you do not know if the train has signal problems or running with good service, so there is a 30% chance the train is having signal problems.