Please prove this theorem.. Theorem 4. The PDF of the F-statistic defined in (14) is given...
4. A sample of size n-81 is taken from an exponential distribution with the pdf f(x)-Be-6x, θ > 0, x > 0. The sample mean is i-35. Find a 95% large- sample confidence interval for θ using the Central Limit Theorem.
Problem 4. The median of a PDF fx(x) is defined as the number a for which P(X s a)-P(X > a)-1/2. Find the median of a Gaussian PDF N(μ; σ2).
5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M > M is a TM and 1011 E L(M)}.
3. (14 pts.) Let the sequence an be defined by ao = -2, a1 = 38 and an = 2an-1 + 15an-2 for all integers n > 2. Prove that for every integer n > 0, an = 4(5") + 2(-3)n+1.
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0 (a) What is c? Plot the pdf (b) Plot the edf of X. (c) Find P(X 0.5<0.3).
Question 1 (*** — Pareto distribution (50%)). Let X1,..., Xnfo, where the PDF fo is given by Omo fo(a) = 907 168 >m), 12,0). -1) ang warte model te is a family of Paret in het gewens where m > 0 is known, and 0 € = (2, ) is unknown. The model F = {fo : 0 € O} is a family of Pareto distributions. It is given that E(X1) = m/(0 - 1) and Var(X1) = m20/{(0 -...
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).
Help please! Let Be be Brownian motion and fix to > 0. Prove that By: = Bto+t - Blo; t o is a Brownian motion.
4. Let {Sn, n > 0} be a symmetric Random Walk on Z. with So-0. Defined Y max{Sk, 1 Sk n, for n 2 0, prove, thanks to a counterexample, that Y is not a Markov Chain.
(+3) The pdf f(x) of a random variable X is given by 0, ifx<0 Find the cumulative distribution function F(r