8. Let X1, X20 be independent Poisson random variables with mean 1.(a) Use the Markov inequality to obtain a bound onP20{{x}Xi > 15(b) Use the central limit theorem to approximateP20Xi>¡ > 15}

We are given 20 independent Poisson random variables, each with a mean of 1. We are asked to find a…

Answered: 8. Let X1, X20 be independent Poisson…

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

1. (Markov's and Chebyshev's Inequality) a) Use Markov's inequality to show that for a sequence of positive random variables X1, X2, ... with values in N = {0,1, 2, ...} and lim;00 E[X;] = 0, it holds that lim;» P[X; = 0] = 1. b) Use Markov's and Chebyshev's inequality to give two upper bounds on the probability that an exponential distributed random variable with parameter A (rate) is larger than x. Calculate the bounds explicitly for ) →00 5 and x = 3,
None
Suppose that X and Y are independent random variables each with a x²(4) distribution. Find the moment generating function of U = X +5Y and evaluate the expectation value E(U). State clearly and justify all steps taken. Hint: You may use without proof the fact that the moment generating function of a x²(v) random variable W is Mur-(t) = (-)". 2t
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?
Let X, Y be positive random variables (not necessarily independent). Assuming X, Y have all finite moments, write and explain briefly the most appropriate of ≤, ≥, =, ? in the blank, where '?' means no relationship holds in general. i) E(X³). √E(X²) E(X4) ii) P(|X+Y> 2)_ -¹/E((X+Y) ¹) iii) E[√x +3]. iv) E[E[Y²|X]]. 16 √E[(X+3)] (EY)²
Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X^2 and Y are independent. Note that by symmetry, it will also follow that Y^2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).
Part II: Sections 2.1 - 2.7 8. Assume that X is a geometric random variable with p=0.32. (a) Compute P(X > 13[X > 3). (b) Compute E(X²).
Let X₁, X₂ be independent and identically distributed random variables following a geometric distribution with parameter p € (0, 1), that is, P(X₁ = k) = pk-1(1-p) for k € N. a) Derive a formula for P(X₁2 k) for ke N. b) Determine the cumulative distribution function of Y = min(X₁, X₂). c) Let Z= max(X₁, X₂). Are Y and Z independent? Justify your answer.
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

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

8. Let X1, X20 be independent Poisson random variables with mean 1. (a) Use the Markov inequality to obtain a bound on P 20 {{x} Xi > 15 (b) Use the central limit theorem to approximate P 20 Xi> ¡ > 15}