Question

Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 635 to 665 nm. What is the mean and variance of the wavelength distribution for this radiation?

Answer 1

The mean of the wavelength distribution for this radiation is 650 nm and the variance is 75 nm².

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

`M = (a + b)/(2)`

The variance is:

`V = ((b-a)^(2))/(12)`

Uniformly distributed at integer nanometers in the red spectrum from 635 to 665 nm.

This means that
`a = 635, b = 665`

Mean

`M = (635 + 665)/(2) = 650`

Variance:

`V = ((665 - 635)^(2))/(12) = 75`

The mean of the wavelength distribution for this radiation is 650 nm and the variance is 75 nm².