1) Consider a memoryless discrete-time source which emits a sequence of random elementsX1, X2, ·where xk for each integer k can be any of a1, a2, az and a4. Assume...that Prob(xka1) = 0.01, Prob(xka2)0.1 and Prob(xkаз)= 0.3. Answer thefollowing questions:b) What is the (simplest) relationship between the entropy of xk and the entropy of(Xk, Xk+1)?

Answered: Image /qna-images/answer/28221ffb-b900-4dee-86bf-bd9c5367a01a.jpg

Answered: Consider a memoryless discrete-time…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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V. (10) The following table of 850 students shows those that have or don't have covid-19 and shows those who had a positive test or a negative test. I just made this data up so don't take this as representative of our current state. Answer the following questions. Negative Test 5 Positive Test Have Covid-19 45 Don't have Covid-19 25 775 Let D be the event you Don't have Covid-19 and N the event you have a negative test. 1. P(D) = 2. P(D I N) = 3. Are D and N independent? 5. What is the probability that you Have Covid-19 even though the test came back negative? 4. Explain TI-84 Plus TEXAS INSTRUMENTS
In a Binary Symmetric (Communication) Channel (BSC) data is sent data is sent using bits 0 and 1. Whenthe source and the destination are far apart, there are repeaters that decode the bit and transmit generate asignal. However due to noise, there decoding error, i.e., there a probability α that a bit 0 will be decodedas (and hence transmitted) as 1. Similarly, β is the probability that a bit 1 will be decoded as (and hencetransmitted as) 1. Let X0 be the bit’s initial parity and and let Xn be the bits parity after the nth repeater.1. Construct the one-step transition matrix for this Markov Chain.2. Suppose the input stream to this communication channel consists of 80% 0s and 20% 1s. Determinethe proportion of 0s and 1s after the first repeater.3. Under the same input values as in (b) determine the proportions of 0s and 1s exiting the 5th relay.
A jury pool has 23 people that are married and 21 people that are not married, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random without replacement, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.) (a) all married people. (b) all not married people. (c) 8 married and 4 that are not married. (d) 6 married and 6 that are not married.
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through k (d). Males Females Total Nursing majors 93 700 793 Non-nursing majors 1015 1723 2738 Part 3 of 4 Total 1108 2423 3531 P(not being female or being a nursing major) = (Round to the nearest thousandth as needed.). (a) Find the probability that the student is male or a nursing major. P(being male or being nursing major) = 0.512 (Round to the nearest thousandth as needed.) (b) Find the probability that the student is female or not a nursing major. D P(being female or not being a nursing major) = 0.974 (Round to the nearest thousandth as needed.) (c) Find the probability that the student is not female or a nursing major. H C n 101 √₁ Vi L (0,0) 4 x
Suppose we know that 0.1% of the population is infected with COVID-19 (the probability that a randomly selected individual is infected with COVID-19 is 0.001). We have a test for COVID-19 that is 99.9% accurate (if the person is infected, then the probability of being tested as POSITIVE is 0.999; if the person is NOT infected, the probability of being tested as NEGATIVE is 0.999) What is the probability that Draco is actually infected with COVID-19, given that he has tested positive? Hint: Draw the appropriate tree diagram and use Bayes' Theorem.

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