Suppose X,,X,,...,X, is a random samples from normal distribution with mean, µand variance,ΣΧi=11 and. XLet Y,,Y2,.., Y, be an independent chi square distribution, each with 1ndegree of freedom. State the distribution and parameter(s) of each of the following randomvariables.17b) K=È(x, - x}*i=1

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Answered: Suppose X,,X,,...,X, is a random…

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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Say you have two sets of data X1, ..., X10 and Y1,..., Y40. All of this data is considered independent. The first set of data are Normally distributed with mean B and variance 10. The second set of data are Normally distributed with mean y and variance 10. We are trying to estimate 0 = X = X; 18 + y. Consider the estimate ô = }X + Ÿ where 3 4 iX + Y where 10 vi=1 1 10 and Y = E Y;? 40 vi=1 40 (a) What is the mean, variance and distribution of 0? (b) What is the probability that 0 is larger than 1 away from 0? (c) What is the bias, variance and MSE of the estimate 0 for estimating 0?
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
Explain at least two differences between the following two point estimations of the population variance. 22 = Σ'1(X, – X)2 n-1 62 _ Σ 1 (X - X)2 =1 = n
A researcher that wanted to estimate the expectation AY of a random variable Y got three independent observations, Y, Y, Y The researcher knows the value o, of the variance of Y and is considering the following estimators: Pi = 4) Yi + (+) ¥ Py = () Yn + (;) ¥½ + () Y½ in (}) Yi + (}) ¥z + (() %D Which of the following is correct? ONone of the above Ois an unbiased estimator of l and it has the smallest variance of the three estimators. Ois an unbiased estimator of µ and it has the smallest variance of the three estimators. O and i, are both unbiased estimators of fl and Var (ſîz) < Var (îì3). is an unbiased estimator of µ and it has the smallest variance of the three estimators.
Let X1, X2, X3, ..., X, be a random sample from a distribution with known variance Var(X,) = o², and unknown mean EX, = 0. Find a (1 – a) confidence interval for 0. Assume that n is large.
7
1.) Consider the discrete random variable with pmf: P(X=x)=(A/(4^x)), x=2,3,4,5,.... What is the value of A?

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