Question 4: A binary communication system transmits signals through an Additive White Gaussian Noise (AWGN) channel. The system can select between uncoded and code modes. In coded mode, channel coding using a linear block code is used. The generator matrix of the code is given as: 100 G = Assuming the Gaussian noise w has following probability density function (pdf): S(w) a) Construct the Maximum Likelihood decoding rule for the coded case b) Find the error probability when the specific codeword of c =[1110] is transmitted
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- 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.Consider the OLS estimator β^j. Under the Gauss-Markov assumptions, a) the estimator has the properties stated in the other three possible answers. b) the estimator is consistent. c) the estimator is the best linear unbiased estimator. d) the estimator is asymptotically normally distributed.Consider the pictured Gauss elimination
- Which of the following statements about logit and probit models is true? (I) They cannot be estimated by ordinary least squares (II) They can be estimated using maximum likelihood (III) They can be estimated using non-linear least squares (IV) They can be estimated using instrumental variables. (a) I only (b) I and II only (c) I, II, and III only (d) I, II, III, and IV.1. Define a Stochastic process and briefly discuss the meaning of measurability of a stochastic process. 2. Consider the ARMA(1,1) model yt = 0.8yt-1 + et + 0.5et-1 with et ~ WN(0, σe2). Derive the Wold representation of yt. 3. Consider the ARMA(2,1) process Φ(L)Xt = Θ(L)et with Φ(L) = 1 − 1.3L + 0.4L2 , Θ(L) = 1 + 0.4L and et ∼ WN(0, σe2). Obtain its Wold representation. 4.Consider the ARMA(2,2) process given by Xt =0.4Xt−1+0.45Xt−2+et+et−1+0.25et−2 with et ∼WN(0,σe2). 5. Consider the MA(1) process yt = et+1.5et−1 with et ∼ WN(0,σe2). Is the above MA(1) a Wold representation? Why or Why not? If not, obtain a suitable Wold representation.A researcher completes a chi-square test for independence and obtains X2 =6.2 for a sample of n=40 participants. a. If the frequency data formed a 2 X 2 matrix, what is the phi-coefficient for the test? b. If the frequency data formed a 3 X 3 matrix, what is the Cramer’s phi-coefficient for the test? c. Explain why a very small value for an expected frequency can distort the results of chi-square test.
- Subject: Stochastic process Question 1 is attached to the image section belowIn the B&K model of Example 18.5-1, suppose that the interarrival time at the checkout area is exponential with mean 5 minutes and that the checkout time per customer is also exponential with mean 10 minutes. Suppose further that will add a fourth counter. Counters 1,2, and 3 will open based on increments of two customers and counter 4 will open when there are 7 or more in the store. (a) The steady-state probabilities, for all . (b) The probability that a fourth counter will be needed. (c) The average number of idle counters.1- The number of items produced in a factory during a week is known to be a randomvariable with mean 50● Using Markov's inequality, what can you say about the probability that this week'sproduction exceeds 75?● If the variance of one week's production is equal to 25, then using Chebyshev'sinequality, what can be said about the probability that this week's production isbetween 40 and 60?
- Question 3. Recall that the discrete stochastic process {Xn, n = 0, 1, 2,...} is a Markov chain if for each n, P(Xn+1 = j|Xn = i, Xn-1 = in-1,..., Xo = io) = P(Xn+1 = j|Xn = i) = Pij. Let {Xn, n = 0, 1, 2,...} be a Markov chain, does the following hold as well? P(Xn+2=jXn = i, Xn-1 = in-1, ..., Xo = io) = P(Xn+2 = j|Xn = i) Give a proof if you think it is true, otherwise give a counterexample. Hint: You may use the law of total probability for conditional probability without proof. Please step by step answer.Consider a simple model of the hunting behaviour of a fox. In a single day, the fox catches either 0 or 1 rabbits, with probabilities 0.3 and 0.7, respectively. The outcome of hunting on day m is independent of all other days.We describe this system through a discrete-time, discrete-state stochastic process R(m), where R is the total number of rabbits caught between the end of day 0 (defining a starting point of our observation) and the end of day m. m = 0,1,2,3... is thus a discrete time parameter, and R(0) = 0 by definition (a) It can be shown that pr(m) – the probability of catching R = r rabbits in m days – is given by a binomial distribution (see Appendix A.2.1). Here, m is the number of “trials”, r the number of successes and q = 0.7 the probability of success. Hence give expressions for:i The mean number of rabbits caught after m days. ii The standard deviation of the total number rabbits caught after m days. iii The standard deviation of the mean number of rabbits caught per day…Question 23: The National Institute of Mental Health published an article stating that in any one-year period, approximately 9% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 10% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 9% in the general adult American population. Test the relevant hypotheses using a 10% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: Based on the hypotheses, find the following: Test Statistic = p-value = Based on the above we choose to The correct summary would be: that the true proportion of people in that city suffering from depression or a…