Assume that the wavelengths of photosynthetically active radiations(PAR) are uni

Question

Assume that the wavelengths of photosynthetically active radiations(PAR) are uniformaly distributed at integer nanometers in the redspectrum from 675 to 700nm. a) What is the mean and variance of the wavelengthdistribution for this radiation? b) If wavelengths are uniformaly distributed at integernanometers from 75 to 100 nm, how does the mean and variance of thewavelength distribution compared to the previous part?Explain. a) What is the mean and variance of the wavelengthdistribution for this radiation? b) If wavelengths are uniformaly distributed at integernanometers from 75 to 100 nm, how does the mean and variance of thewavelength distribution compared to the previous part?Explain.

Explanation / Answer

a.
a = 675
b = 700

mean = (a+b)/2
= 687.5

variance = ((b-a)^2) / 12
= 52.083

b.
a = 75
b = 100

mean = 87.5
variance = 52.083

Both parts have same variance because range (=25) is same but mean is part 1 is larger than that in part 2.

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