Let X1,..., Xn be iid random variables with the density function f(x;0) = (0+ 1)xº for 0

The useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. Determine a) The half life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)

Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X2,..., X be a random sample of size n from the population of X. (a) Write down the likelihood function of the parameter. (b) Show that the log likelihood function of depends on the sample only through Σj=1 Xj. (c) Find the maximum likelihood estimator (mle) of 0. (d) Find the method of moments estimator (mme) of 0.