Let X bea randomvariable having the uniformdistribution onthe interval(θ,θ+1),θ∈R.Show thatX isnot complete.
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A: To find the moment estimator of a, we equate the sample moment to population moment.
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A: Given : Z= 3 W +10 Where W is uniformly distributed on the interval [0,5].
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Let X bea randomvariable having the uniformdistribution onthe interval(θ,θ+1),θ∈R.Show thatX isnot complete.
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- Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.The probability that Paul’s train to work is late on any day is 0.15, independently of other days. (i) The number of days on which Paul’s on which Paul’s train to work is late during a 450-days period is denoted by the random carriable Y. Find a value of a such the P(Y>a)≈ 1/6 . In the expansion of (0.15+0.85)^50 , the terms involving 0.15^r and 0.15^(r+1) and denoted by Tr and Tr+1 respectively. (ii) Show that Tr / Tr+1 = 17(r+1)/3(50-r)
- Does a distribution exist for which:Mx(t) = (t)/(t-1)for |t| < 1? If yes, find it, otherwise prove that is not possibleUse the moment generating function to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n.Find the distribution of Y = X1 + · · · + Xn.Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.
- Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere ] What is the joint CDF of X and Y? Note: F(x,y) = P(X<=x, Y<=y) = ∫ ∫ f(x,y)dxdyLet X be uniformly distributed on the interval [−1, 1], and Y = X2(a) Give fX(x).(b) Determine FY (y).(c) Determine fy(y).Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane.Hint: You must prove that there are pairs of points, arbitrarily close together, on which thevariation of F is large, for example, (n, 0) and (n + 1/n, 0).