Question

Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 675 to 695 nm. What is the mean, ?, and variance, ?2, of the wavelength distribution for this radiation? Round your answers to one decimal place.

mean, ? =

variance, ?2 =

Answer 1

Mean=685

Variance=36.7

Explanation:

The mean of uniform discrete distribution can be expressed as the average of the boundaries

mean=( b+a)/2

The variance of uniform discrete distribution can be expressed as the difference of the boundaries decreased by 1 and squared, decreased by 1 and divided by 12.

σ²=[(b-a+1)^2 - 1]/12

We were given the wavelength from from 675 to 695 nm which means

a= 675, b= 695

We can now calculate the mean by using the expresion below

mean=( b+a)/2

Mean=( 675 + 695)/2

=685

The variance can be calculated by using the expression below

σ²=[(b-a+1)^2 - 1]/12

σ²=[(695-675+1)^2 -1]/12

σ²=440/12

σ²=36.7

Therefore, the the mean and variance, of the wavelength distribution for this radiation are 685 and 36.7 respectively