4. Given a random variable w with density F(w) and a random variable p as the umiform im the interval (-71, +71) where wlP (two w and p are independent) R.V.S Suppose the stochastic process, xt) = a Cos (wt+P). %3D a) show that xlt) Wss with zero mean ond auto correlation equal R(E) = E(Coswe) 2 j(wt+P) b) show that zt)=aë is also Wss.

4. Given a random variable w with density F(w) and a random variable p as the umiform im the interval (-71, +71) where wlP (two w and p are independent) R.V.S Suppose the stochastic process, xt) = a Cos (wt+P). %3D a) show that xlt) Wss with zero mean ond auto correlation equal R(E) = E(Coswe) 2 j(wt+P) b) show that zt)=aë is also Wss.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section17.5: Steady-state Probabilities And Mean First Passage Times

Problem 6P

See similar textbooks

Similar questions

What is the likelihood ratio p(x|C₁) p(x|C₂) in the case of Gaussian densities?
It is known that a natural law obeys the quadratic relationship y = ax“. What is the best line of the form y = px + q that can be used to model data and minimize Mean-Squared-Error if all of the data points are drawn uniformly at random from the domain [0,1]? r* ur, a,
In Sammon mapping, if the mapping is linear, namely, g(x|W) = WTx, how can W that minimizes the Sammon stress be calculated?
Conditional Probability How do I find P(A) and also P(B) given P(C) P(C') P(AlC) P(BlC) P(AlC') and P(BlC'). And how do I find out if P(A) and P(B) are independent?
Problem 1 (14 points)Show that the autocovariance function can be written asγ(s, t) = E[(xs − μs)(xt − μt)] = E(xsxt) − μsμtwhere E(xt) = μt and E(xs) = μs
10. Let W be a wff. If no free occurrence of the variable x in W (x) is in the scope of a quantifier that binds a variable in t, then we say the term t is... (A) out of bounds (C) bound to x (B) free to replace x in W (x) (D) a solitary term
Question 5: Minimize the following boolean function K map: F(A, B, C, D) = Em(0, 2, 8, 10, 14): Σd(5 , 15 )
Using the nonlinear programming (steepest decent) method, we want to estimate the parameters of an ARMAX model whose polynoomials are given in the following. A(q¯¹)=1+qq¯¹ + a₂q² +a;q³ B(q¯¹)=b₁q¹ C(q¹)=1+c₁q¹+c₂q²² u(t) Assume that we have some parametric observations as →B(¹) U = [u (1),u (2),u (3),u (4),u (5),u (6),u (7),u (8)] Y = [y (1),y (2), y (3), y (4), y (5), y (6), y (7), y (8)F C(q-¹) 1 A (q-¹) v(t) y (t) Considering whole steps of the mentioed method such as initial selection and updating of the parameters' value (one updating step is required in addition to the initialization step), write all the necessary relations and parameters in respect to the obserations in a parametric and simplified form as possible.
A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 . f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0 (a) Using M_{X}(t) or otherwise, find the mean and variance of X. (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.
:Determine the probability transition matrix ∥Pij∥ for the following Markov chains. Pleaseprovide the solutions step by step and provide a short explanation for each step. => 3 black balls and 3 white balls are placed in two urns so that each urncontains 3 balls. At each step one ball is selected at random from each urn and thetwo balls interchange. The state of the process is the number of white balls in thefirst urn.
J 2 Suggest a Bayesian prior for a probabilistic ellipse slice. The slice should be normally distributed points in the area between two non-intersecting ellipses such that I need to generate points from such an area, (maybe using a distribution like the Kotz-type distributions). Answer with a python code for generating the points and an image that shows the result. The solution should use the covariance matrix between two variables and the mean vector of two entries.
Write a short computer program to calculate CV for an Einstein solid and show these resultsas a graph of Cv/Nk vs. kT/epsilon. Include three scenarios: The q << N and q >> N limits and also the more general case which is applicable for "any" q