EconomicsLet A be a "random point" that coincides with the point a1, a2, a3 or a4 with equal probabil-ities.a31-1Ya20as1 aiXLet a random variable X be the first coordinate of the point A, a random variable Y be thesecond coordinate of the point A.(d) Compute E[X] and E[Y].(e) Compute Var[X], Var[Y], Cov(X, Y), Corr (X, Y).(f) Find the conditional distribution of Y given X = -1,0, 1.(g) Compute E[Y|X = −1], E[Y|X = 0], E[Y|X = 1].(h) Characterize a random variable E[Y|X].(i) Verify the Law of Iterated Expectations by checking E[Y] = E[E[Y|X]].(j) Is the point with coordinates (E[X], E[Y]) in the support of A?(k) Are the random variables X and Y correlated? Independent? Discuss.(1) What would the joint distribution be if the random variables X and Y are independentand their marginal distributions do not change.

Given:In this problem, we are dealing with a random point A that can coincide with one of four given…

Answered: Let a random variable X be the first…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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N(0, o?) is For the simple linear model Y = a + BX + €, where the error variable e ~ independent of X, use the law of total variance to show that Var(Y) = 3² Var(X)+o².
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Find E (XY) where X and Y are independent U (0, 1) random variables.
Let W₁ < W₂ < ... < Wn be the order statistics of n independent observations from a U(0, 1) distribution. (a) Find the pdf of W₁ and that of Wn. (b) Use the results of (a) to verify that E (W₁) = 1/(n+1) and E(Wn) = n/(n+1).
The joint distribution of X and Y is: Pxy(0,0)=1/25, Pxy(0,1)=a, Pxy(0,2)=2/25 Рxy(1,0)-а, Рx(1,1)-b, Рҳ/(1,2)-а Рxy(2,0)-2/25, Рxx(2,1)-а, Рҳ/(2,2)-1/25 You want "a" to make the variance of Y as minimum as possible. X,Y X,Y 1. Fir The variance of Y equals. Tin Select one: а. 1/2 b. 6/25 с. 2/5 d. 3/5 e. 3/10
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Suppose that X, Y and Z are independent. The expected value is given by E(X) = 0, E(Y) = 1, E(Z) = 5 We also know that the variance is given by Var(X)=1, Var(Y)=1, Var(Z)=25 The values of the covariance are Cov(X,Y)=2, Cov(Y,Z)=1 Which of the satements are true? 1. Cov(ex,Y2 + 1) = 0 2. Е(XY)-1 3. If a and b are real numbers then Cov(aX+bZ, Y+Z)=2a+25b 4. Cov(X,Y)=0
Let X be a point randomly selected from the unit interval [0, 1]. Consider the random variable Y = (1-X)-¹/2 (a) Sketch Y as a function of X. (b) Find and plot the cdf of Y. (c) Derive the pdf of Y. (d) Compute the following probabilities: P(Y > 1), P(3 < Y < 6), P(Y ≤ 10).
The time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let T1 and T2 be two independent waiting times for this distribution. Find expected time between each call and variance. (E(T) and V(T)) Find the probability for both T1 and T2 to be greater than one.
Let X and Y be independent and N(0, 1) distributed random variables. Let U = X and V = X/Y. Show that the random variable V is Cauchy distributed and find E(V ).
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