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

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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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3. Let X1, X2, ..., Xn be a random sample from the population N(µz,0²) and Y1, Y2,...,Ym a random sample from the population N(µy, o2), where both means (z and Hy) are assumed known. Note that the two distributions have a common variance of o². (a) If the X's and Y's are independent, show that the MLE for the common variance is: E (Xi - H2)² +E(Y; - Hy)? n+ m (b) Is the MLE found above unbiased for o2?
6. 4 married couples bought 8 seats in the same row for a concert. How many different ways can they sit: a) Without restriction? b) If each couple will sit together?
Suppose that the response y is generated by y = f(x) + €, where e is a zero-mean Gaussian noise with variance 1. a) Suppose that f(x) = x. Randomly generate 10 x's and generate the corresponding y's; you need to generate two random numbers (i.e., x and e for each of the 10 points). Fit the data with linear regression and plot the scatter points. b) Suppose that f(x) = x². Randomly generate 10 (x, y) pairs. Fit the data with linear regression and plot the scatter points. c) Suppose that f(x) = 1/x. Randomly generate 10 (x, y) pairs. Fit the data with linear regression and plot the scatter points.
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There are 3000 stocks in the long-short stock market, which will be traded for 250 days in the next year. Set X and Y to be the daily holding amount of each stock And the return of the next day, and X and Y are respectively sampled from the normal distribution of N (0.100000NO, 2E-2). Use enough data to estimate Calculate the R2 of X and Y linear regression to be 001. Assume that positions among stocks are not correlated, and returns between stocks are not correlated. Define a day’s PNL as the day’s receipt beneficial PNL= 3000∑xy Find the expectation of PN and the sharpe rate of PNL every day
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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 X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn
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1. Consider the following regression model y = x3 + u. (1) Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss- Markov assumptions are: • MLR.1: The true model in the population is given by (1). • MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n} following the population model in (1). .... • MLR.3: No one explanatory variable can be written as a linear combination of the remaining explanatory variables that is, there is no perfectcollinearity. • MLR.4: In the population, the error u has an expected value of zero given any values of the explanatory variables, that is Elu|x] = 0. • MLR.5: In the population, the error u has the same variance given any values of the explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant. In the following scenarios, state whether 3 is an unbiased and consistent estimator of 3, and provide a brief justification for your answer in each case - but no formal mathematical…
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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?