A Markov chain {x}=0,1,2,.. satisfies the difference equation X =Axk-1 for every k ≥ 1, where- (0.9A ={)0.8 0.60.2 0.4(i) Find the general term x for k≥ 1.(ii) What happens to x as k→ ∞o?- (0.3).and Xo =

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Answered: A Markov chain {x}=0,1,2,... satisfies…

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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3. Let X ~ Exponential() and let t be a constant with 0 0 be any value. (a) Calculate P(X > b) exactly. (b) Now suppose we didn't know the answer to (a), i.e., we could not calculate P(X > b) exactly. Recalling that E(X)= , use Markov's inequality to establish an upper bound on P(X > b). (c) Next we'll apply Markov's inequality in a different way. First, calculate E(etx). (d) Next, use the Markov inequality to prove a bound on P(etX > a) (here a > 0 is any positive number, while we assume 0 b) (here b > 0 is any positive number, and again 0 b) as in part (a), the upper bound on P(X > b) as in part (b), and the alternative upper bound on P(X > b) as in part (e). How close are these upper bounds to the real probability? Which bound is better? Try this for a few values of X, b,t and describe what you see. 6.
Determine a and b such thatp(x) = x2 +ax+ bsatisfies p(l) = 0 and p' (1) = 4.
The result of the convolution; y(t) = 7e-5t y(t) = L-1{(7/(s+5))*e-S} y(t) = L-1 {(7/(s+5)).e-S} = L-1{7e-S/(s+5)} Ⓒy(t) = (7/(s+5)).e-S Ⓒy(t) = 7e-S/(s+5) 7e-5tu(t) * 5(t-1) can be written via the Laplace transform as
Q.6 Show that: **Y B(x+1, y) = B(x, y) 1. 1, T(x+-)) 3, 4x+1 Q.7 3 Show that : B(x+,x+= (x+1)B(x+x)
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Example 7-18. Show that eitx =1+ (eit – 1) x(1) + (eit – 1)². T+.. x(2) 2! + (eit – 1)r. r! + where x(r) = x (x- 1) (x – 2) ... (x - r + 1). Hence show that d Ho' = [D ¢(t)]t = 0, where D =7c eith and H is the rth factorial moment.
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A Markov chain {x}=0,1,2,... satisfies the difference equation x = Ax-1 for every k ≥ 1, where 0.8 0.6 A-(0506) = 0.2 0.4 (i) Find the general term x for k 21. (ii) What happens to x as k→ ∞o? and Xo = (0:3).