5. Let Y1 < Y2 < Y3 be the order statistics of a random sample X1, X2, X3 from the distributionwith pdff(x):1exp02x – 0102, х > 01, — о < в1 < 00, 02 > 0.(a) Find the joint pdf of Z1 = Y1, Z2 = Y2 and Z3 = Y1 + Y2 + Y3.(b) Find the joint sufficient statistics for 0 and 02.%3D

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Answered: 5. Let Y1 < Y2 < Y3 be the order…

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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What is the variance and standard deviation for the number of times the SAT is taken? x Frequency (f) fx f*x2= (f*x) x (x) (4) = (3)x(1) 5152727-(2547473)(2547473)/1518859=880035.3688/1518859=0.5794 (1) (2) (3)=(1)x(2) (4)=(3x1) Population Variance 1 721,769 721,769 721,769 2 601,325 1,202,650 2,405,300 3 166,736 500,208 1,500,624 4 22,299 89,196 356,784 5 6,730 33,650 168,250 Total 1,518,859 2,547,473 5,152,727 880035.3688 0.5794 n=1,518,859 ∑fx = 2,547,473 The population variance is 0.5794 The Standard Deviation? 0.76 Can you show me the steps to reach the standard deviation of .76 ?
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
The information associated with the maximum likelihood estimator of a parameter 0 is 4n, where n is the number of observations. Calculate the asymptotic variance of the maximum likelihood estimator of 20 . (A) (В) (C) (D) 8n (E) 16n
Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)
For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish

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5. Let Y1 < Y2 < Y3 be the order statistics of a random sample X1, X2, X3 from the distribution with pdf 1 x - 01 f(x) = exp x > 01, - 0 < 01 < ∞, 02 > 0. 02 02 (a) Find the joint pdf of Z1 = Y1, Z2 = Y2 and Z3 = Y1 + Y2 + Y3. (b) Find the joint sufficient statistics for 01 and 02.