Suppose that X1,..., Xn are i.i.d. N (0, 5) with density f (x, 0) = V27 x € R, 0 > 0 where 0 is an unknown parameter. The prior T(0) on 0 is assumed to be Gamma(4, ) with the density of a Gamma(a, B) given by: T(8) 1 ga-1 e, a, ß > 0. T(a)Ba a) Find the maximum likelihood estimator for 0. 1 X2 Ô mle 1 Ômle ΣΧ Ômle Ômle = X2

Suppose that X1,..., Xn are i.i.d. N (0, 5) with density f (x, 0) = V27 x € R, 0 > 0 where 0 is an unknown parameter. The prior T(0) on 0 is assumed to be Gamma(4, ) with the density of a Gamma(a, B) given by: T(8) 1 ga-1 e, a, ß > 0. T(a)Ba a) Find the maximum likelihood estimator for 0. 1 X2 Ô mle 1 Ômle ΣΧ Ômle Ômle = X2

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose that the joint probability density function of X and Y is fx,y(x,y) = 78.125(x² - y²) e-5x, for 0
A random process {X(t)} is given by X(t) = A cos pt + B sin pt, where A and B are independent RVs such that E(A) = E(B) = 0 and E(A²) = E(B²) = o². Find the power spectral density of the process I %3D
Given the Rayleigh random variable with density function show that the mean πρ V4 E[X] =a + CS Scanned with CamScanner f(x) -(x-a)² b 2 =(x-a)e u(x -a)
(11) When the conditional density of X given Y = y E (0, 1) is 2x fx\Y=y (x) = y < x < 1. 1 – y² ’ Compute E(X|Y = 0.25). 0.7 0.25 0.75 None of the above N/A (Select One)
Suppose X and Y have joint probability density function flx.v.zl= a(x*+ xyz),0
Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by 3y2 0 < y< 0, f (y|0) = өз 0, elsewhere. 1.1. Show that Y(n) max(Y1, Y2, ... , Yn) is sufficient for 0.
3. Let f be the density function of a random variable X, and let Y = (Y1, Y2, Y3) be a continuous random vector with density function %3! fY (y1, V2, ys) 6 f(v)f(v)/() 1{vn < ya < ya}. (a) Find the conditional density fy, Y,Y, (V, Vsly2) and argue that (Y I. Y) | Y. (b) If X has a uniform distribution on the unit interval (0, 1], deduce that (Y, Y) | (Y = V) has a certain bivariate uniform distribution. Over which set?
2. A particle of mass, m, has the wavefunction given by: (x, t) = Ce-a[(mx²/h) + it] . (a) Sketch Re [(x,0)] as a function of x. (b) Sketch Re [p(0, t)] as a function of t. (c) Sketch the probability density for finding the particle at x at t = 0. (d) Explain the time dependence in the probability density for locating the particle in space. (e) Find C (f) Find (x) (g) Find (x2) (h) Find ox (i) Find (p) (j) Find (p?) (k) Find op (1) Is the product, O,0, consistent with the Heisenberg uncertainty principle? (m) Find T
(1) Find the constant c in the following bivariate density. Scz' y? if z € (-1,1) and y e (x², 1) f(x,y) := if otherwise. The correct answer is 24/7 24 7 4/27 27/4 N/A (Select One)
Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x (Ə ln(f(X;0) nE
The density function of X is given by f(x) = = (a + bx2, 0 ≤x≤1 0, elsewhere If E = [x] = = find a, b
1. The joint density for the random variables (X, Y) is given below. for 0SS1,0SySI 0. for clsewhere (a) Find the marginal density of X (b) Find the marginal density of Y (c) Find VarlX] (d) Find VarV] (e) Are X and Y statistically independent? () Find P(X>0.6) (R) I EXY-0.8, find the correlation between X and Y