7.80. (Stationary Distribution.) If (π;) are stationary probabilities for (X+), thenwe have seen that \To = μπ₁, and for j ≥ 2,=(λj + μj)πj = λi−1πi−1 + µj+1πj+1.(7.41)Show that Tk=λολη-1με... με•ΠΟ If C =1 + x=1λολη-1με...μη< ∞, show that thestationary distribution is given by ñ = 1/C and(7.42)πn =1 λοC με ...μηAn-1n ≥ 1.'

the equation in the image you sent because it relies on specific details about a stationary…

Answered: 7.80. (Stationary Distribution.) If…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 24E

See similar textbooks

Similar questions

Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).
EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.
Suppose Y · Uniform(01,02) where the parameters and O2 take the values -1 and 2 respectively. Compute the probability P(Y < y) when y=1.41.
Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2).(a) What is the distribution of rt(8) = rt + rt−1 + rt−2 +...+ rt−7?(b) What is the covariance between r7(3) and r9(3)?(c) What is the conditional distribution r17(3) given that r16 =0.004 (d) What is the probability that the gross return over the first 10 times periods is at least 1.05?
4. Suppose that X has pdf f(x) = 3x² for 0 < x< 1. Find the pdf of the random variable Y = VX.
Consider a mixture of two Gaussian distributions, 0.AN([12]. [i])+0.GN([8]. Compute the marginal distributions for each dimension. Compute the marginal distributions for each dimension. • Compute the mean and mode for the two-dimensional distribu- tion. [8.4 2 2 1.7
2. Y1, Y2, ..., Yn are i.i.d. exponential random variables with E{Yi} = 1/θ. Find thedistribution of Y =1 nPiYi.
1.2. Assume that Billy's driving time to class is uniformly distributed from 15-20 minutes in good weather, and uniformly distributed from 25-30 minutes in bad weather. Let the RV X describe Billy's drive time. If the probability of good weather is 2/3. a) .describe mathematically the PDF of X. b) ..describe graphically the PDF of X. c) .find the probability that Billy's drive time is >18 minutes. d) .find the Expected Value of Billy's drive time, irrespective of the weather.
4. If XN3 (μ, 2) where uT=[2-3 1] and E= 1 3 2 1 2 21 then find the distribution of 3X₁ - 2X2 + X3, where a= [3 -2 1].
Q.7 For an exponential distribution fx(x; 4) = {4e*; Sue Hx, x 2 0 e.w. where u > 0 Write (Don't derive) (a) Mean (expected value), i.e. EX). (b) Standard deviation, i.e. S. D. (X). (c) Moment generating function, i.e. Mx(t). (d) Cumulative distribution function (cdf), Fx(x). of Nizy
21. Let the random variable X have the moment generating function e3t M(t) : -1
Q3. Generate three random variates according to each of the following distributions using your own uniform random variates from U(0, 1) and list them: • Discrete Uniform: U (15, 17) • Uniform: U (0.57, 1.5). • Triangular: Triang (2, 10, 4). • Binomial: Bin (12, 0.4). • Lognormal: LN (5, 1). Beta: Beta (5, 5). • Negbin (8, 0.4) • Weibull (.5, 2.5) Geom (0.5) • PT5 (0.5, 0.5)

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS