Question

Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 625 to 655 nm. What is the mean and variance of the wavelength distribution for this radiation

Answer 1

Answer: The mean and variance of the wavelength distribution for this radiation are 642.5 nm and 75 nm.

Explanation:

The mean and variance of a continuous uniform distribution function with parameters m and n is given by :-

`\text{Mean=}(m+n)/(2)\\\\\text{Variance}=((n-m)^2)/(12)`

Given :
`m=625\ \ \ n=655`

`\text{Then, Mean=}(625+655)/(2)=642.5\\\\\text{Variance}=((655-625)^2)/(12)=75`

Hence, the mean and variance of the wavelength distribution for this radiation are 642.5 nm and 75 nm.