Problem 1.Let X(t) be a wide-sense stationary Gaussian process with mean ux = 10 and autocovariance function4Cxx(T):9 + 72Compute P(X(5) > X(1) +1.9).

GivenX(t) b a wide sense stationary Gaussian Process.μX=10The auto Covariance function…

Answered: Problem 1. Let X(t) be a wide-sense…

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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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following. 1 2 3 p(y) 0.55 0.25 0.15 0.05 (a) Compute E(Y). E(Y) = (No Response) (b) Suppose an individual with Y violations incurs a surcharge of $120Y. Calculate the expected amount of the surcharge. $ (No Response)
b) Let X(t) be a zero mean, stationary, Gaussian process with autocorrelation function R (T). This process is applied to a square law device defined by the input-output relation Y(t) = X(t), where Y(t) is the output. i) Show that the mean of Y(1) is R (0). ii) Find out the autocovariance function of y(t).
2. We would like to fit a linear regression estimate to the dataset {(x®,y@),(x), y),., (x(N), g/N)} with x e RM by minimizing the ordinary least square (OLS) objective function: N M -Συ, .(i) J(w): j=1 Specifically, we solve for each coefficient wk (1< k < M) by deriving an expression of Wk from the critical point J(w) the dataset (x(1), y(1)), (x(2), y(2)), . 0. What is the expression for each wk in terms of … , (x(^), y(N) and w1, , wk-1, Wk+1; *** , WM? .. .. Select one: E, (y() –D,-1,j+k W;x;") i=D1 Wk = =1 O Wk
2. Suppose that X₁, X2, and X3 are mutually independent and identically distributed with moment generating function (m. g. f.) given by M(t). Then, the m. g. f. of X₁ + X2 - 2X3 is given by {M(t)²M(2t)}. True or false, give reason for your answer.
5. Find the linearization L(x) of f at a = 0 1 f(x)%3= V2+x a = 0 %3D Select the correct answer. 1 a) L(x): V2 4V2 b) L(x) = -+ 1 4/2 c) L(x) = -- %D V2 4/2 d) L(x) = V2 – 4V2x e) none
2. Using the linear model of a researcher calculated the hat-matrix = X(X'X)¯¹X' = H = TA [0.2516 0.1101 0.3931 0.1101 0.2044 0.0157 0.3931 0.1572 0.7704 0.0535 0.2421 -0.1352 0.1101 0.2044 0.0157 0.2421 0.0818 0.2232 -0.0597 0.2799 (a) Estimate o. That is, find Residual Standard Error s. /1.) zachy UNDI Yevevi TA' y = Bo + Br2 + H and the residual e using 6 observations. vull lalg 0.0818 0.0534 0.1101 0.2421 0.2044 0.2233 -0.1352 0.0157 -0.0597 0.3176 0.2421 0.2233 0.2044 0.22327 0.2233 0.2516 SOUD DAN wuc. " e = -0.02 0.12 -0.56 0.88 -0.01 [-0.07]
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Problem 1. Let X(t) be a wide-sense stationary Gaussian process with mean ux = 10 and autocovariance function 4 Cxx(T) 9 + 7² Compute P(X(5) > X(1) + 1.9).