Specify each of the following. (a) The conditional distribution of X,, given that X2-X2 for the joint distribution with, μ1-0,P2-2, σ11-2, σ22-1, and P12:5 (b) The conditional distribution of X2, giv...
Need step by step explanation with the formula used. Following is my question that has been answered: I received the following answer to the questions. However, I do not understand what formula was used in part b and c. Could anyone help me to understand the solution with more details? Thanks! Specify each of the following. (a) The conditional distribution of X,, given that X2-X2 for the joint distribution with, μ1-0,P2-2, σ11-2, σ22-1, and P12:5 (b) The conditional distribution of...
1-1 postmultiply by . Take inverses of the resulting expression. -A22A21 I 4.13. Show the following if X is N,(. E) with 0. (a) Check that |E= |2 2||E,, - E, 2E . (Note that | can be factored into the product of contributions from the marginal and conditional distributions.) (b) Check that (x- μ ) Σ (x-μ) - [x1- μιΣι2 Σ7. (x2-μ.)]. - μ "Σ1,Σ3(x2 μ)1 x (Σ1-ΣΣΣ1 + (x -μ2), Σ( X2-μ) (Thus, the joint density exponent can...
Problem 2. (Conditional Distribution of MVN) Let Z1, Z2, Z3 be i.i.d. N(0,1) dis- tributed random variables, and set X1 = 21 – Z3 X2 = 2Z1 + Z2 – 223 X3 = -221 +3Z3 1) What distribution does X = (X1, X2, X3)T follow? Specific the parameters. 2) Find out P(X2 > 0|X1 + X3 = 0).
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
Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b) Calculate the conditional distribution of Xi given Y-n for n 2 0. Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b)...
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 3 1 0.5 1 E [X]-μ | 0 | and var(X)=Σー| 0 0.5 | com pute: 2 c) var(X2-X3 (d) var(X2 + X3) (e) cov(4X2 +X1,3Xi - 2X3)
Question 15: Let Π is distributed as Uniform(0, 1) and the conditional distribution of X given Π = π is Bernoulli (π). Find the conditional distribution of Π given X = x. Question 15: Let Π is distributed as Uniform(0, 1) and the conditional distribution of X given 11 = π is Bernoulli (π). Find the conditional distribution of Π given X = x
1. [10 marks) Let X, and X, have joint density function f(0,0%) = cca 110, x2 > 0,8 +29 < 1, where c is a constant. Find: (a) (2 marksThe value of c. (b) (2 marks] E(XX). (c) (2 marks] P(X1 < 3X2). (a) (2 marks] (2016). (e) (2 marks] E(X1/X3 = 5).
4. Let X1,X2, x 2) distribution, and let sr_ Ση:1 (Xi-X)2 and S2 n-l Σηι (Xi-X)2 be the estimators of σ2. (i) Show that the MSE of S" is smaller than the MSE of S2 (ii) Find ElvS2] and suggest an unbiased estimator of σ. n be a random sample from N (μ, σ
Let X = (X1, X2) be a 2 x 1 random vector having joint pdf (1 x € (0, 1) ~ [0, 1] 10 otherwise. Find the probability P(X1 < 0.5, X2 < 0.5)