Let X(t) and Y(t) be defined by X(t) = Acoswt + Bsinwt and Y(t) = Bcoswt – Asinwt3where w is a constant and A and B are independent random variables both having zero mean andvariance. Find the cross correlation of X(t) and Y(t). Are X(t) and Y(t) jointly W.S.S|processes?Consider a random process X(t) defined by4X(t) = Ucost + (V + 1)sint.

# given two stochastic process X(t) & y(t) then to find cross correlation between x (t) and…

Answered: Let X(t) and Y(t) be defined by X(t) =…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e E [0, ). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 %3D where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: w-α+ βR and so the employee is guaranteed a payment a and then a bonus payment ßR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: Eu(w\e) = E(w\e)-eV ar(w]e) – c(e) where E(wle) and Var(wle) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the disutility of…
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Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i=1,..., n.
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5. (a) Establish the formula: nroxdy = n,r,0x, Oy, + n2r20x,Oy, + n,dx,dy, + nzdx,dy2 Where dx, = x - i, dy, = 91 - y, dx, = X2 - X, dy, = y2 - y 5. (b) Find the correlation coefficient of combined sample given that %3D %3! Sample Size Mean of X Var(X) Mean of Y Correlation between X and Y Var(Y) Group 1 n = 100 i, = 80 ox? = 10 y, = 100 o = 15 %3! = 0.6 Group 2 n2 = 150 = 72 Ox = 12 y, = 118 o = 18 2 = 0.4

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Let X(t) and Y(t) be defined by X(t) = Acoswt + Bsinwt and Y(t) = Bcoswt – Asinwt %3D 3 where w is a constant and A and B are independent random variables both having zero mean and variance. Find the cross correlation of X(t) and Y(t). Are X(t) and Y(t) jointly W.S.S processes?