1. Let X1 and X2 have the joint pdf f(x1, x2) = 2e-11-22, 0 < 11 < 1 2 < 0o, zero elsewhere. Find the joint pdf of Yı = 2X1 and Y2 = X2 – Xı.
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.
anwer this ..The answer must be?? 2.3.3 Let f(2), 0 of Xi and X2. 1, zero elsewhere, be the joint podf of X1 and X2 (a) Find the conditional mean and variance of X1, given X2 = 22, 0 < x2 < 1. (b) Find the distribution of Y E(X1|X2). (c) Determine E(Y) and Var(Y) and compare these to E(X1) and Var(X1), Te spectively
3. Let (X1, X2) have the joint p.d.f 1 if 0 <1,0 < <1 f(1, ) else Find P(X1X2 < 0.5)
Let X1, X2,..., Xn be a r.s. from f(x) = 0x0-1, for 0 < x <1,0 < a < 0o. (a) Find the MLE of 0. (b) Let T = -log X. Find the pdf of T. (c) Find the pdf of Y = DIT: (i.e., distribution of Y = - , log Xi). (d) Find E(). (e) Find E( ). (f) Show that the variance of 0 MLE → as n → 00. (g) Find the MME of 0.
Let X1 and X2 have joint PDF f(x1,x2)=x1+x2 for 0 <x1 <1 and 0<x2 <1.(a) Find the covariance and correlation of X1 and X2. (b) Find the conditional mean and conditional variance of X1 given X2 = x2.
6.4.3. Let X1, X2, ..., Xn be iid, each with the distribution having pdf f(x; 01, 02) = (1/02)e-(2–01)/02, 01 < x <ao, -20 < 02 < 0o, zero elsewhere. Find the maximum likelihood estimators of 01 and 02.
Let X1 and X2 be independent and have the same pdf that is given by f(t)=2t when 0 < t < 1 and zero otherwise. Find the probability P(X1/X2 < 1/2).
kercise 6. (Rossi 2.6.4, 2.6.29) (a) Let X - (X1, X2) be a random vector with probability density function given by f(x1,x2) = 24x1x2 with support determined by 0 < xit x2 < 1,띠 > 0,x2 > 0 Determine each of the following. (v) Var(Xi/X2) (vi) ElVar(X1|X2)]
Suppose X1 and X2 are continuous random variables with join pdf given by f(x1, x2) = 2(x1 + x2) if 0 < x1 < x2 < 1, and zero otherwise. (a) Find P(X2 > 2X1). (b) Find the marginal pdf of X2. (c) Find the conditional pdf of X1 given X2 = x2.