The Rayleigh probabilty density function is the special case of the Weibull probability density function, when alpha a, the Weibull shape parameter, is 2. that is, a Rayleigh random variable, X has probability density function. f(x)=( 2x) (e^-x^2/b)/B x> or equal to 0 and 0 elsewhere , and where B>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 for a wind turbine.

a) find E)X

b) find Var (X) .

c) If B = 100

d) find P(X<10)