Let X₁, X₂ X₁ be arandom Sample Of Siat nFrom the population X. Suppose that X has thefollowing probability mass Function.€(1) Based onFOL.B) = {0ofthe(1) Find the conditional distribution.likelihood Function given the function of theStatistics, G = [X₁. Apply F(L(0)|g(6:0)1) above is Q =Xi a Sufficientanswer0(1-0²²²-1 € = 1,2,3EisewhereJustify your(iii) Show whether orEstimator?notof the parameterX is a consistentB

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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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u is an unbiased estimator of the parameter X. Select one: O True O False On average, 5 traffic accidents per month occur at a certain intersection. What is the probability that in any given month at this intersection exactly 4 accidents will occur? no accident will occur? The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable X having a continuous uniform distr B= 10.7. The probability that on a given day the amount of coffee dispensed by this machine will be at most 6.2 liters is Select one: O 0.704 100.112 10 0.274 1.726
Let X1, , Xn be iid with population density Je (z Sx(x) = r > 0, otherwise. Here 0 is an unkown population parameter. Show that X-0 has an Exponential(1) distribution. Find the method of moment estimator for 0. Let's call this 6. Is ôj unbiased for 0 ? Explain with precise computation. Find the maximum likelihood estimator for 6. Let's call this Ô2. Is ô, unbiased for 0 ? Explain with precise conputation.
5-9 Simplify Equation (5.28) for the special case where the primary distribution N is Poisson with parameter A.
3. Consider a pdf f so that a random variable X~ f has expected value E[X] = 3 and variance V[X] = 10. Now consider n = 10 i.i.d. random variables X1, X2,..., X10 drawn from f. Let X = 10 (a) What is E[X]? (b) What is VIX]? (c) What is the standard deviation of X? (d) Which is larger PX > 4] or P[X > 4]? 10 ₁=1 Xi.
2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following distribution function Where, ß > 0. 1 f(x; 0) = B 0, e (x-4) B for x > 4 otherwise f) Is the maximum likelihood estimator of the parameter ß unbiased or not? g) What is the maximum likelihood estimator of g (B) = 2(B + 1). h) Is the maximum likelihood estimator of g (B) = 2(ß + 1) unbiased or not?
When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=
A random sample of size n1 = 15 is selected from a normal population with a mean of 75 and a standard deviation of 9. A second random sample of size n2 = 9 is taken from another normal population with mean 69 and standard deviation 15. Let X1 and X2 be the %3D two sample means. Find: (a) The probability that X - X2 exceeds 3. (b) The probability that 4.9 < X – X2 < 5.9. Round your answers to two decimal places (e.g. 98.76). (a) i (b)
2. Assume X ~ Exp(0), so that its pdf is 1 f(x; 8) x > 0,0 < 0 < o. e We have 5 samples, 1,2,3,4, and, 5, under Exp(0). Find the maximum likelihood estimator of 0 using the five samples.
Suppose X1, X2, ... , Xn is a random sample and Xi = {1, with probability p 0, with probability 1-p} for every i = 1, 2, ... , n. Find the Moment Generating Function of ∑i=1n Xi . What is the distribution of ∑i=1n Xi ?
The geometric distribution gives the probability that the first success occurs at the xth trial with success probability p. f(x)=(1-p)x-1p, x=1,2,3,... Show that E(X)=1/p
Consider data 5,1,3,5,5,4,3,2 of the Poisson distribution with expectation u. We want to test H0:u=u0 with u0=2. Write the log-likelihood for the data under H0 and the likelihood ratio A(y) for testing H0
A random sample of size n₁ = 14 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second random sample of size n₂ = 9 is taken from another normal population with mean 71 and standard deviation 11. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ – X₂ exceeds 4. 1 2 (b) The probability that 4.3 ≤ X₁ – X2 ≤ 5.6. Round your answers to two decimal places (e.g. 98.76). (a) i (b) i

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