Could someone help me solve this question and show all work
Could someone help me solve this question and show all work 7. Let X = (x1,.....
7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n >0 in probability if nP(Xn > n) -» 0. (b) Find a random variable Y satisfying nP(Y > n) ->0 and E(Y) = Oo
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Any help would be appreciated! Problem 4 Let (X, Y)~ N and Z = X1(XY > 0}-X1(XY < 0} (1) Find the distribution of Z (2) Show that the joint distribution of Y and Z is not bivariate normal.
could someone please help me solve this and show the steps in the calculator as well?? thank you!! 2. The following information is gathered from a bivariate dataset: Xbar = 12, sx - 3, ybar = 60, sy = 7.5, r=-0.8. (a) Write the equation of the least-squares regression line. (b) What fraction (percentage) of the variation in y is explainable by variation in x? (c) An individual data pair is (15, 49). State the residual for that data pair....
7. Let X1,... , Xn be iid based on f(x; 6) -22e-z?/e where x > 0. Show that θ=-yx? is efficient
Hello can someone help me answer this please Suppose that X (X1,X2, . . . , X.) ald Y-(Yİ,%, , Y,n) are random samples from continuous distributions F and G, respectively. Wilcoxon's two-sample test statistioc W- W(X,Y) is defined to be X/Ri where Ri is the rank of Y in the combined sample. 1. Let T Z, where Z, Z2,, Zm are numbers sampled at random without replacement from the set {1,2,...,N) Show that E(Z) = (N + 1)/2 and...
Let X be a 4-dimensional random vector defined as X = [X1 correlation matrix X4' with expected value vector and X2 X3 E[X] =| | , 1 1 -1 0 Rx-10-11-1 0 0 0-1 1 Let Y be a 3-dimensional random vector with (a) Find a matrix A such that Y -AX. (b) Find the correlation matrix of Y, that is Ry (c) Find the correlation matrix between X1 and Y, that is Rx,Y
$ 200, if x > 10 else 3) Let X1, X2,..., X, bei.i.d. random variables from a population with f(x;0) = 0 > 0 being unknown parameter. a) Sketch a graph of a density from this family for a fixed 0. b) Find the cumulative distribution function F(x;0) of X1. c) Show that X (1) is a minimal sufficient statistic for e. 2n02n o d) Show that the density of X(1) is given by fx y2n +T, if y (y;0)...
(d) Let (x1,x) R..9x 2 yo} (3) S is the set of combinations of (x,x2) which produce at least output level yo.Economists refer to S'as the upper contour set associated with output yo. Assume that x (x,x2) S and y (y,y2) S. That is xfx yo and yy z yo. i) Let z (z1,z2) R.. What must be true for ze S? ( mark) ii) Let z= (z1,z2) x +(1A)y where 02<1 Prove that zE S Hint: Using results on...
Please answer all the parts neatly with all details. 8. Let X1, X2, ... be an i.i.d. with Xn Let Y min(X,... , Xn) + 1 and Zn = max(X1,... , Xn) - 1. (a) Show that Y, - 0 and 0 - Z, have the same distribution uniform(0 1,0+ 1) (b) Show that Y, -P>0. (c) Show that n(Yn - Zn) converges in distribution and specify the limit distribution