The continuous random variable X is uniformly distributed over the interval (2.5, 3.5] a) Calculate E(X)

b) calculate var(x) Give your answer to four decimal places.

please solve this

Let X1,...,X, be independent random variables with pdfs -{* 0 -i(0 – 1) 0. Find a two-dimensional sufficient statistic for 0.

Exercise 10. For an exponential random variable X (Definition 10), show that E[X] = }. More generally, for a function o : R R, E(¢(X)] = | (u) dF(u) (5.4)

Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?