2- Let the probability density function of the random variable X is- {²()*Then My(t) is(a) 2(3-e¹)-1(c) 2e¹(3-e¹)-1f(x) =‚x = 1,2,3, ...0 , otherwise(b) 3(2 – e¹)-¹(d) e' (3-e¹)-1aO

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Answered: 2- Let the probability density function…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A simple random sample X1, …, Xn is drawn from a population, and the quantities ln X1, …, ln Xn are plotted on a normal probability plot. The points approximately follow a straight line. True or false: a) X1, …, Xn come from a population that is approximately lognormal. b) X1, …, Xn come from a population that is approximately normal. c) ln X1, …, ln Xn come from a population that is approximately lognormal. d) ln X1, …, ln Xn come from a population that is approximately normal.
b) Let Y1, Y2, ..., Yn be a random sample from a population with probability density function in part a). Show that the best test for the hypothesis in part a) rejects Ho if |yi <c i=1 where c solves the probability equation a = P(II1Yis c[0 = 2). c) Let X1,X2, ..., Xn be a random sample from GAMMA(2,ß) distribution, and consider Y = E-,Xi- Show whether or not Y is a pivotal quantity and give its distribution.
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2- Let the probability density function of the random variable X is - {²()* Then My(t) is (a) 2(3-e¹)-¹ (c) 2e¹(3-et)-1 f(x) = ‚ x = 1,2,3,... , otherwise (b) 3(2-e¹)-1 (d) e' (3-e')-1 O