3 3. (a) Show how Chebyshev's InequalityP(\X – H| > Cơ)< efollows by Markov's Inequality (which was proved in class).(b) Suppose that we repeatedly flip a fair coin. Using Chebyshev's Inequal-ity, find an upper bound on the number of flips required so that wecan be 99% sure that the proportion of Heads will be in the interval[0.49,0.51] (close to 50%).

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Answered: 3. (a) Show how Chebyshev's Inequality…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
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?
Suppose that X k is a time-homogenous Markov chain. Show thatP{X3= j3, X2= j2|X0= j0,X1 = j1}= P{X3 = j3 | X2 = j2} P{X2 = j2|X1 = j1}.
2-Discuss in detail about "MARKOV'S PROCESS"
A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?
A manufacturer has a machine that if it ran all day today has a proba- bility of 0.2 of breaking down sometime during the day tomorrow. When the machine breaks down, it goes offline for the remainder of the day and then a technician will spend the next day (after the breakdown) repairing it. A newly repaired machine only has a proability of 0.1 of breaking down sometime tomorrow. (a) Formulate the evolution of the status of the machine at the end of the day as a Markov Chain by identifying the three possible states at the end of the day and providing the transition probabilities between these states. (b) Determine the expected first passage times, µij , for all combinations of states i and j where i cannot equal to j (i.e., you don’t need to determine the recurrence times). You must provide the set of equations used to calculate these µij (micro with lowercase i and j). (c) Using your results from (b): (i) Identify the expected number of full days that the machine will remain…
SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.
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Consider a continuous time Markov chain with three states {0, 1, 2} and transitions rates as follows: q01 = 3, q12 = 5, q21 = 6, q10 = 4 and the remaining rates are zeros. Find the limiting probabilities for the chain.
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One can use the equations of the Markowitz model to derive the CAPM equation. At thispoint, one would be wrong to conclude that this is the CAPM model. What additional argumentis necessary to make the transition from one model to the other?a. All other options are necessary.b. There is a single investor who holds the mean-variance efficient portfolio.c. There is at least one investor who holds the market portfolio.d. Investors know the returns and standard deviations of all securities in the economy.
why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion

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