Q4) A Markov source as given in the table below:siS2S3P(S1)=0.2P(S2)=0.2P(S3)=0.6PI2=0.3P21=0.3P31=0.35P13=0.4P22=0.7P32=0.3Draw Markov diagram thenCalculate1) Average source Entropy?3) Prove that: G,>G;

We have to find out : Average source entropy We have to prove that : G1>G2

Answered: Q4) A Markov source as given in the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2.5 10. pls help
Markov model: d = 33% (success) f = 19% (non-success) 1. Assuming previous success [1 0], what is the probability of having a successful year? 2. What is the probability of having two successful years?
[stochastic process1]
• General notation for Markov chains: P(A) is the probability of the event A when the Markov chain starts in state x, Pμ(A) the probability when the initial state is random with distribution μ. Ty = min{n ≥ 1: X₂ = y} is the first time after 0 that the chain visits state y. Px,y = Px(Ty < ∞) . Ny is the number of visits to state y after time 0. 4. Let Sn, n20 be a random walk on Z with step distribution 1-p 2 P 1) = 1/², P(X₁ = 1) = 2/₁ 2' 2' P(X₂ = 0) P(X₂ = − 1) = for some 0 < p < 1, p ‡ / . We may denote q=1 - p. That is, the increments (X₂)₁ are i.i.d. and S₂ = X₁ + … + Xn for n ≥ 1 and S = 0. Compute E[S2+1 Sn] for n ≥ 1. (b) Show that Mn = (q/p) Sn defines a martingale (with respect to (Xk)k-1). (c) Does the limit limn→∞ Mn exist almost surely? If yes, give a justification. If your answer is no, explain why. (d) Let T be the first time that S is equal to either −3 or 3. Compute P(ST = 3). Hint: You may use, without proof, the fact P(T<∞) = 1 and that the Optional Stopping Theorem…
a)
C)
What are the difficulties in estimating the following model? Use as much detail as possible in answering this question while considering the Gauss-Markov assumptions and OLS estimator. Economic productivity = β0 + β1Unemployment + β2Innovation + θiControls + ei Where unemployment is the average unemployment rate of a country and innovation is an index of R&D performance.

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Q4) A Markov source as given in the table below: si S2 S3 P(S1)=0.2 P(S2)=0.2 P(S3)=0.6 PI2=0.3 P21=0.3 P31=0.35 P13=0.4 P22=0.7 P32=0.3 Draw Markov diagram then Calculate 1) Average source Entropy? 3) Prove that: G,>G;