Originally Posted by
kevek 1)Let X be a continous random variable with a uniform distribution on the range (0,θ). Find the mean and variance of X, along with its distribution function F(x)=P(X<=x).
2)suppose X1...Xn are independent identically distributed random variables, each with distribution function Fx(x). Let M be the largest of the {Xi}. express the event 'M<=x' as an intersection of n independent events, each involving exactly one of the {Xi}. hence deduce that the distribution function of M is Fm(x)=[Fx(x)]^n
3)use results of 1) and 2) to write down expression for the distribution function of the largest among n independent U(0,θ) random variables. find the corresponding density function.