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- For Cramer’s V, values close to 0 indicate a strong association.dik koordinatylarda x,y öyleki x kare artı y kare küçüktür beş denkleminin grafiğini çizinizLet X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?
- Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.Show that under the assumptions of normal multipleregression analysis(a) E(Bˆ i) = βi for i = 0, 1, ... , k;(b) var(Bˆ i) = ciiσ2 for i = 0, 1, ... , k;(c) cov(Bˆ i, Bˆ j) = cijσ2 for i Z j = 0, 1, ... , k.Let X1, . . . , Xn i.i.d. U([θ1, θ2]), i.e., X1, . . . , Xn are independent and follow a uniform distribution on the interval [θ1, θ2] for θ1, θ2 ∈ R and θ1 < θ2. Find an estimator for θ1 and θ2 using the method of moments.
- Given that Y1, Y2, Y3, ..., Yn is a random sample from a gamma distribution with parameters alfa = 3, and Beta = theta, find the mle of theta.Suppose that Yt follows the Moving Average process of order 1 (MA(1)) model Yt=ϵt−θϵt−1, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=σϵ2 . a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations ofSuppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)
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