The number of hours, N, of daylight at a certain location can be expressed as N(d)=12+6sin(2πd/365) where d=day of the year starting with March 21. (a) What is the probability distribution function for hours of daylight if you assume the day of the year is a random variable? (b) What is the average number of hours of daylight at that location over the year? (c) If the energy production, E, of a certain solar thermal energy facility at that location is dependent upon the number of hours of daylight and is found to be E(N)=107N calories per day, f • what is the expected daily energy production over the year from that facility? • what is the standard deviation of the energy produced? • what is the variance of the energy production?