Let {Xt; t≥ 0} be astochastic process. Ifthe joint distributionof Xt₁, Xt₂,..., XtnandXtX₁₁+h₂ X ₁₂+h₂..., X₁₁+his the same tn samefor all h> 0; then theprocess isSelect one:a. Weak stationaryprocessb. Markov processC.O Strong stationaryprocessd. Process withindependentincrements.

Let {Xt : t≥0} be a stochastic processes If the joint distribution of Xt1, Xt2,....Xtn and Xt1+h,…

Answered: Let {Xt; t≥ 0} be a stochastic process.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

2. Given the cumulative distribution function of a discrete random variable, X as F(x)= dx-2) (c-1x x= 3,4,5,6 (a) Find the value of constant c. (b) Evaluate P(X <4) (c) Find the mode. (d) Calculate the value of E(X) and E(x²). (e) Hence, find E(1–2X) and Var(1–2X).
Suppose I flip n independent biased coins such that the jth coin has probability j/n of being heads, for j = 1,...,n. Let Hn be a random variable equal to the total number of heads. (a) What is the expectation of H,? (b) What is the variance of Hn? (c) Use Markov's inequality to derive an upper bound on P(Hn 2 9n/10).
Let a stochastic process (Xt) be given as follows: Xt = 3 + 0:5Xt-1 + t, where (t) is white noise with var ( t) = 1. a) What process is (Xt)? b) Explain briefly why this is a \conditional expectation" model, but not a \conditional variance" model. c) Suppose we observed Xt = 2:5, Xt-1 = 1:7. Compute a forecast for Xt+1. d) Suppose we observed Xt = 2:5, Xt-1 = 1:7. Compute a forecast for the variance of the process at time t + 1, that is, for the variance of Xt+1.
2. Let X₁, X2, ..., Xn represent a random sample from a Poisson distribution with probability mass function given below. p(x) = e-11e0 el x! summary sheet on Moodle and state E(X). X 2 (a) Look up the Special Distributions (b) Find the moment estimator of X. (c) Show that the maximum likelihood estimator of X is the same as the moment estimator. x = 0, 1, 2, ... (d) Estimate A from the following observations using the moment/maximum likelihood. estimator. Round your answer to 4 decimal places. Frequency 18 0 1 2 3 4 5 6 7 37 42 30 13 7 2 1
3. A random variable X has a cumulative distribution function if 0 0.5). (e) Find P(X < 1.25). (f) Find P(X = 1.25).
Pedestrians approach a crossing from the left and right sides following independent Poisson processes withaverage arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a lightis flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right orfrom right to left). Assume that the left and right arrival processes are independent, that the light flashesevery T = 2 minutes, and that crossing takes zero time – it is instantaneous.1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are allcrossing from left to right?
Could you solve (i), (ii), (iii)? Thank you.
Q1: Let X have p.d.f f(x) : =7,x = 1,2, 3 and X1 and X2 are stochastically 6. independent. Let Y1 = X,X2 and let Y2 = X2. Find g(y1, y2)and g,(y1). ***********************: ************: ******************
b) Let X₁, X₂,..., X and Y₁, Y₂, ..., Ym be random samples from populations with moment generating 25 functions Mx₁(t) = ³t+t² and My(t) = (₁-¹)²5, respectively. i) Find the sampling distribution of the statistic W = X₁ + 2X₂ − X3 + X4 + X5. ii) What is the value of the sample size n, if P[Σ1(X¡ − X)² > 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Ỹ - µy| ≥10) < 0.04?
1. (a) lind autocovariance function and autocorrelation function of Poisson Process. (b) If X(1) = A cos ct+ Bsin et and Y) and B are uncorrelated random variables with mean 0 and variance 1. Examine whether {X(1)} and {Y(!)} are jointly widen -sense stationary or not. Bcoset - Asin ct. where c is a constant, A
12. Consider a M/H2/1/FCFS/00/00 queue in steady state. Here H2 means that the service-time distribution is two-stage hyperexponential. Let A be the arrival rate, and , the service rate of stage i (i = 1, 2). Suppose that the customer goes to stage 1 with probability of 0.5. Give an appropriate definition of the system state and draw the state transition diagram. Write down the global balance equations for the general state and solve them using z-transforms. %3D
1. Suppose that for a stochastic variable X~B(n;p) with the parameters n =10 and p = 30% a) BY HAND (PICTURE MUST BE UPLOADED): Calculate the mean and the standard deviation b) Use IT to determine P(X = 4).

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS