Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle...
Problem 2. Let f be a self-map on a set X. For x,y e X define x ~ y if and only if f"(x) = f(y) for some integers n, m > 0. Show that ~ is an equivalence relation.
Show the resistance looking into the base ro= 0 PA + B + 1)RE >RE (b)
Let X1, ..., Xn be a random sample from the distribution 1 f(x; 01, 02) e-(2–01)/02 x > 01, - < 01 <0, 02 > 0. 7 02 Find the method of moments estimators (MMEs) of 04 and 02.
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
. c) + < 2 b) 2 + 3x 27, 0. Solve for r: r' + 2.r < 2.1? +12
5. Let S be a non-empty bounded subset of R. If a > 0, show that sup (aS) = a sup S where aS = {as : s E S}. Let c = sup S, show ac = sup (aS). This is done by showing: (a) ac is an upper bound of aS. (b) If y is another upper bound of aS then ac < 7. Both are done using definitions and the fact that c=sup S.
5. Show that if an >0 and an is convegent, then ln(1 + an) is convergent.
2. Show that for > 0, we have x4 + IV
When X1, X2, ..., X, is a random sample from Uniform(0,26) (only >0), show that (X(1), Xn)) is sufficient statistic for 0.
2. Let X 1, , Xn be iid from the distribution modeled by 8-2 fx (1:0)-(9. θ):r"-"(1-2) dr where 0 < x < 1 and θ > 1 Find the MME (method of moments estimate/estimator) for 0