Answer:
The Rayleigh distribution is often used to model wind speed distribution. It is characterized by a scale parameter, often denoted as "σ" (sigma), which depends on the average wind speed.
The probability density function (PDF) of the Rayleigh distribution is given by:
f(x; σ) = (x / σ^2) * e^(-x^2 / (2σ^2))
Where:
f(x; σ) is the PDF of the Rayleigh distribution with scale parameter σ.
x is the wind speed.
σ is the scale parameter.
In your case, you have an average wind speed of 8 m/s. To calculate the wind speed distribution using the Rayleigh distribution, you need to determine the appropriate value of σ.
The relationship between σ and the average wind speed (V_avg) is given by:
σ = V_avg / √(π/2)
Substituting the average wind speed of 8 m/s into the formula:
σ = 8 m/s / √(π/2)
σ ≈ 8 m/s / 1.2533 ≈ 6.37 m/s (approximately)
Now that you have the value of σ, you can use it to describe the Rayleigh distribution for your average wind speed of 8 m/s. This distribution will describe the probability of various wind speeds occurring around the average wind speed of 8 m/s.
Step-by-step explanation: