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Problem 10: 10 points Assume that a sample {X;:15; <4} of size 4 is drawn from...


Problem 10: 10 points Assume that a sample {X;:15; <4} of size 4 is drawn from the uniform distribution Unif(-1,1). Consider
Problem 10: 10 points Assume that a sample {X;:15; <4} of size 4 is drawn from the uniform distribution Unif(-1,1). Consider the maximal order statistic, X(4). 1. Derive density function of X(4) 2. Evaluate expectation of X(4) 3. Determine variance of X(4)
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TOPIC:Distribution of the maximal order statistic.

Problem -10% Here, {x; : 14; 44} be a random sample of size 4, from w(-1,D distribution So, the pdf of x; is - x; (x) = { t =D Define, tu = max. { x 1, X2, -, Xu). So, the edf of tens is - * Fx (x) = P(xcw, 32). tew ex = P ( x, EX , X₂ EX , - , X 4 2So, So, Ido (x) = (x+13 10.x4 -12 X El. otherweise (Ans 2X We need = E(X), - lad, (x) dx . *S (2=3° de * *(2843*** 32-) de (3ix we need, var [Xew L den body - + [ *(4) de +(\** (62+ 32 + 32-) de -|(2++32 + 3+ + 2) +(94*** -1 -So, var [X4) [x2] – ² {xon). 0.106 75 Tans

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Problem 10: 10 points Assume that a sample {X;:15; <4} of size 4 is drawn from...
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