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5. Let f(x) = cosx where 0<x< . Find the optimal step size h if the...
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for any a, 0 < a < 1. b. Does {f,) converge uniformly on [0, 1]?
Please do this step by step because the explanation is a huge part
of the grade.
< x < and 3. Let X be a random variable with p.d.f. fx(x) = (1/2)e-Axl where - X>0. Let Y = X?. Find the c.d.f. and the p.d.f. of Y.
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find the solution of X"' + 2x' + x=f(t), t> 2.
5. Let X1,...,Xn be a random sample from the pdf f(\) = 6x-2 where 0 <O<< 0. (a) Find the MLE of e. You need to justify it is a local maximum. (b) Find the method of moments estimator of 0.
How to solve it?
Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
Find the exact radian solutions in the interval 0 < x < 211 of the equation sinx-cosx-1)(cosx - 3) -0.
Let f(x)= kx + 5 x-1 for x<2 for x > 2 . Find the value of k for which f(x) is continuous at x=2.
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
let X be s random nareprion if x <0 > 0 (a) Let M= {X > 1). Find Fx( M)
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).