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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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…
Consider the following consumer function an answer: (Picture)
a)
A student would like to describe whether wage depends on gender. There are two models estimated by OLS with (Male =1 for males and 0 for female) and (Fermale =1 for females and 0 for males) included: %3! Model 1:wage, = Bri +P2 Female, + E Model 2:wage, = Bm1 + Bm2 Female, + Emi %3D %3D Choose the correct sentence: O a. Bm2 = -Pn O b. Bn+ Pn= Bal Oc. Bmi + Bm2 = B1 %3D O d. All expressions are correct
C)
For the following Markov models: a ito dove b) find the stationary probability distribution on paper, SUre 5A An ion channel can be in either open or closed state. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. 5B An individual can be either susceptible or infected, the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. 5C The genotype of an organism can be either normal (wild type) or mutant. Each generation, a wild type individual has probability 0.03 of having a mutant offspring, and a mutant has probability 0.005 of having a wild type offspring.

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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;