The Rayleigh probability density function is the special case of the Weibull probability density function, when alpha, 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) for 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 beta = 32 find P(X < 4).