Let X be a r.v. on interval (1,a) where a>1 if E[x]=6 varx, find a.
Let X be a r.v. with probability density function f(x)-e(4-x2), -2 < otherwise (a) What is the value of c? (b) What is the cumulative distribution function of X? (c) What is EX) and VarX
Let X be a Gaussian r.v. with mean 5 and sigma 10. Let Y be an independent exponential r.v. with lambda 3. Let Z be an independent continuous uniform r.v. in the interval [-1,1]. a. (5) Compute E[X+Y+Z]. b. (5) Compute VAR[X+Y+Z].
Let X1, ..., X, € [X], where X r.v. with pdf 0.00-110.1) (2) w.r.t. the unknown parameter 6 > 0 Find the m.l.e. and MLE of 0.
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).
5.7 Let X, X, be independent r.v.'s from the u(e -a, o+ b) distribution, where a and b are (known) positive constants and θ Ω M. Determine the moment estimate θ of θ, and compute its expectation and variance.
Practice Exam Questions 2 Let X be a r.v. with density function x 2 1 a. Determine the distribution function of X, i.e. F(x). Find E(X) and V(X) b. Find the MLE estimator of θ constructed from a sample Xi,Xn c. Is the estimator find in (b) biased? Practice Exam Questions 2 Let X be a r.v. with density function x 2 1 a. Determine the distribution function of X, i.e. F(x). Find E(X) and V(X) b. Find the MLE...
Let f(x) = 2x + 8/x +1 (a) Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. If the answer cannot be expressed as an interval, state DNE (short for does not exist). (b) Find the relative maxima and relative minima, if any. If none, state DNE. (c) Determine where the graph of the function is concave upward and where it is concave downward. If the answer cannot be expressed as an interval, use...
Let X be a R.V. with a gamma distribution and the following parameters (X~(α, 1)). What is the pdf and the cdf of Y = X/β, where β > 0 . What is the name of this type of distribution?
f (x, θ)-θ(1 _ θ)-1 2.7 Let X be a r.v. having th Then show that X is sufficient for θ , X-1, 2, , θ e Ω (0,1)
4. Let X1, X, be two r.v.'s with m.g.f. given by M(t1, tz)=[] (en+2 +1)+] (e? +e?)]”, t1, tz € R. Calculate E(X1), oʻ(X,) and C(X1, X2), provided they are finite.