In: Statistics and Probability
Let X1, X2, . . . be iid random variables following a uniform distribution on the interval [0, θ]. Show that max(X1, . . . , Xn) → θ in probability as n → ∞
TOPIC:Convergence in probability.
Hence , by the sufficient condition of probability convergence, we can say that, X(n) =max.{ X1,X2,....,Xn} converges to , in probability.(PROVED).