16:47DoneSuppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3..., X, has the following probability density function(exefor x = 0,1,2,...elsewhered)e)f(x; 0) =NLTEx!'0.What is the Cramer-Rao lower bound [for the variance of the unbiased estimator ofparameter 9?17Use the one-parameter regular exponential family definition to find the functions,h(x), c(0), w(0) and t(x).21 PageNиLesese)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the maximum likelihood estimator (MLE) of parameter θ.
Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).
Q3) The joint probability density function of two discrete random variables X and ¥ is given by p(x, y)=c(2x+3y), where x and can assume all integers such that 0 <
Find the moment-generating function of the contin-uous random variable X whose probability density is given by f(x) =1 for 0 < x < 10 elsewhere and use it to find μ1,μ2, and σ2.
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Suppose X and Y are independent and identically distributed (i.i.d.) randomvariables, each with the uniform distribution on [0, 1]. What is the cumulative distributionfunction and the density function of XY ?
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3) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of parameter ? L Use the one-parameter regular exponential family definition to find the functions. b) (0) -)