Problem 4. WSS and Signal Detection.a. Consider a real Gaussian random sequence x(n), n an integer, withE[x(n)] =0, E[r(n)²] = 1, E[r(n)a(m)] = pln-mwhere 0 < p < 1. Lety(n){x(n)nn‡0n = 0.i. Is x(n) wide sense stationary?ii. Find the covariance of y(n) and state whether or not it is widesense stationary.

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Answered: Problem 4. WSS and Signal Detection. a.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 15. Herpes simplex-2. Suppose 7.5% of a population is infected with Herpes simplex-2 virus (HSV2). You select seven individuals at random from the population. What is the probability of finding at least one HSV2-positive individual in your sample? [Hint: First find Pr(X = 0). Then make use of the fact that (X ≥ 1) = 1− Pr(X = 0).]
Problem 1: The joint probability mass function of X and Y, p(x,y), is given by: p(1, 1) = 1 9 p(2, 1) = 1 3 p(3, 1) = 1 9 (1) p(1, 2) = 1 9 p(2, 2) = 0 p(3, 2) = 1 18 (2) p(1, 3) = 0 p(2, 3) = 1 6 p(3, 3) = 1 9 (3) (4) Compute E[X|Y = i] for i = 1,2,3.
3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?
Problem 7: Let X be a continuous random variable with the probability density for f(x) = 3x2 values of x in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X.
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…
Question 3 A product is classified according to the number of defects it contains and the factory that produces it. Let X and Y be the random variables that represent the number of defects per unit (taking on possible values of 0, 1, 2, or 3) and the factory number (taking on possible values 1 or 2), respectively. The entries in the table represent the joint possibility mass function of a randomly chosen product.
Question 42, A Gallup Poll showed that 30% of Americans are satisfied with the way things are going in the US. Suppose a sample of 20 Amserican is selected as part of the study of the state of the nation. Compute the probability that exactly 4 of the 20 Americans surveyed are satisfied with the way things are going in the United States Compute the probability that at leeast 2 of the Americans surveyed are satisfied with the way things are going in US. Fro the sample of 20 Americans compute the expected number of Americans who are satisfied with the way things are going in US. For the sample of 20 Americans, compute the variance and standard deviation of the number of Americans who are satisfied with the way things are going in the US.
Question 15: In a recent Super Bowl, a TV network predicted that 90 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 55 people who saw the commercials and found that 48 of them said they would watch one of the television shows.Suppose you are have the following null and alternative hypotheses for a test you are running:H0:p=0.9H0:p=0.9Ha:p>0.9Ha:p>0.9Calculate the test statistic, rounded to 3 decimal places z=

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