1Let X - Beta(a, B) and Y =Beta distribution pdf:fx (x) = cx"-1(1 – x)³-1 for x € (0, 1) and parameters a > 0, B > 0,Γ (α + β)where c is a normalizing constant equal toГ(а)Г(8)(Recall that I'(z + 1) = zT(z) = z(z – 1)r(z – 1) =...)Question part 3:What is EY? Assume that a > 1.hint: again, use the kernel trick.a + Ba – Ba + B111-1+Ba + BWe do not have enough information to answer this question. 1Let X - Beta(a, B) and Y =Beta distribution pdf:fx (x) = cx"-1(1 – x)B-1 for x E (0, 1) and parameters a > 0, B > 0,T(a + B)where c is a normalizing constant equal toI(a)r(8)Recall that I'(z + 1) = zT(z) = z(z – 1)T(z – 1) ==...Question part 1:E X = . What is E[X²]?a+B*hint: using the kernel trick (figuring out a new normalizing constant) will probably befaster than looking up the variance and doing the necessary algebra. Consolidate yourx terms and recognize the new Beta distribution's parameters to figure out itsnormalizing constant.aß(a + B)2 (a + B+ 1)a?(a+ B)2We do not have enough information to answer this question.(a +1)a(a +B+1)(a + B)

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Answered: Question part 3: What is E[Y]? Assume…

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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Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?
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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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Question part 3: What is E[Y]? Assume that a > 1. L triel