The Rayleigh probability density function is the special case of the Weibull probability density function, when %u03B1, the Weibull shape parameter, is 2. That is, a Rayleigh random variable, X has probability density function
\(f(x)=2x/\beta e^{-x^{2}/\beta} x >= 0\)
and 0 elsewhere, and where Beta > 0
The Rayleigh probability density function is a single parameter probability density function and is important as a model for wind speed, and for example is used in estimating energy recovery from a wind turbine. a) Find E(X). b) Find Var(X). c) If %u03B2 = 32 find P(X < 4).