Question

Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 620 to 640 nm. What is the mean and variance of the wavelength distribution for this radiation?

Answer 1

36.66

Step-by-step explanation:

The mean of a discrete uniform distribution is the average of the boundaries:

μ=
`(b+a)/(2)`

The variance of a discrete uniform distribution is the difference of the boundaries decreased by 1 and squared, decrease by 1 and divided by

σ^2=
`((b-a+1)^2-1)/(12)`

a)

Given:

a = 620 nm

b = 640 nm

Use the formulas to determine the mean and variance:

μ=
`(620+640)/(2)=630\\`

σ^2=
`((b-a+1)^2-1)/(12)`

=(640-620+1)^2-1/12

=36.66