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.(adsbygoogle = window.adsbygoogle || []).push({});

(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?

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# Probability distribution function

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