Answered: If the probability transition matrix…

Name: 1 If the probability transitionmatrix is:0.70.10.30.9)The Stationary D
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 1 If the probability transitionmatrix is:0.70.10.30.9)The Stationary Distribution of MarkovChain after long time00.700.30O250.75O300.70O750.25

Math

Statistics

If the probability transition matrix is: 0.7 0.1 0.3 0.9 The Stationary Distribution of Markov Chain after long time 0.70 0.30 O25 0.75 @30 0.70 O.75 0.25

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

See similar textbooks

Similar questions

Find P(X=4) if X has a Poisson distribution such that 3P(X=1)=P(X=2)
If X has the Poisson distribution with P(X=1) = 2P(X=2), then P(X ≥ 2) is approximately:
Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve in R.
A gasoline wholesale distributor has bulk storage tanks that hold xed supplies andare lled every Monday. Of interest to the wholesaler is the proportion of this supplythat is sold during the week. Over many weeks of observation, the distributor foundthat this proportion could be modeled by a beta distribution with = 4 and = 2.Find the probability that the wholesaler will sell at least 90% of her stock in a givenweek.
Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
Assume you have created a 2-stock portfolio by investing $30,000 in stock X with a beta of 0.8, and $70,000 in stock Y with a beta of 1.2. Market risk premium is 8% and risk-free rate is 6%. The followings are the probability distributions of Stocks X and Y’s future returns: State of Economy Probability rx rY Recession 0.1 -10% -35% Below average 0.2 2% 0% Average 0.4 12% 20% Above average 0.2 20% 25% Boom 0.1 38% 45% Calculate the portfolio’s expected rate of return and the standard deviation of its future returns Calculate the required rate of return of your portfolio. Which stock in…
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.
The following are some applications of the Markovinequality of Exercise 29:(a) The scores that high school juniors get on the verbalpart of the PSAT/NMSQT test may be looked upon asvalues of a random variable with the mean μ = 41. Findan upper bound to the probability that one of the studentswill get a score of 65 or more.(b) The weight of certain animals may be looked uponas a random variable with a mean of 212 grams. If noneof the animals weighs less than 165 grams, find an upperbound to the probability that such an animal will weigh atleast 250 grams.
For each of the following transition matrices, do the following: (1) Determine whether the Markov chain is irreducible. (2) Find a stationary distribution π; is the stationary distribution unique? (3)Give the period of each state. (4) Without using any software package, find P200 approximately.
If X(t) is a continuous-time random process with mean value of m and variance of s^2, what is the value of the autocorrelation function at time lag tau=0?
If it is known that the random process X (t) is a stationary process in a broad sense, could the following autocorrelation function belong to this process? Explain the reason for your answer.
Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)