1 Prove that a random q-ary code with rate R> 0 with high probability has relative distance8 > H7'(1 – 2R – E). Note that this is worse than the bound for random linear codes in|Hint : Your argument should show that the probability of having distance at leastdzH-1q(1-2R-e)ōzHq-1(1-2R-e) is 1-0(1)1-0(1), i.e. the probability should go to 1 as the blocklength n→o

Given:: Prove that a random q-ary code with rate R>0 with high probability has relative distance…

Answered: Prove that a random q-ary code with…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 17EQ

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A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.33(2.7)−7(4.2)=−21.3 A 3−7=−43−7=−4 B 2.7−4.2=−1.52.7−4.2=−1.5 C…
If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?
1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?
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Here we have a random walk (with p=1/2) on the integers in the range [0,7] (endpoints 0 and 7 are absorbing). With a full explanation, suggest the expected number of moves to absorption, starting at x0=4.
Determine the mean waiting time W for an M/M/2 system when lambda = 2 and μ = 1.2. Compare this with the mean waiting time in an M/M/1 system whose arrival rate is lambda = 1 and service rate is μ = 1.2. Since the arrival rate per server is the same in both cases and service times don’t vary, should the wait times be the same in both cases?
A new warehouse is being designed and a decision concerning the number of loading docks is required. There are two models based on truckarrival assumptions for the use of this warehouse, given that loading a truck requires 1 hour. Using the first model, we assume that the warehouse could be serviced by one of the many thousands of independent truckers who arrive randomly to obtain a load for delivery. It is known that, on average, 1 of these trucks would arrive each hour. For the second model, assume that the company hires a fleet of 10 trucks that are assigned full time to shipments from this warehouse. Under that assumption the trucks would arrive randomly, but the probability of any truck arriving during a given hour is 0.1. Obtain the appropriate probability distribution for each of these assumptions and compare the results.
A soda company sells one of its soft drinks in 12 ounce cans. In order to ensure that every can has at least 12 ounces in it, the machines in the factory are set to fill each can with an average of 12.1 ounces of soda. Every week, a quality-control technician tests 10 cans to make sure that the average amount of soda in the cans is still 12.1 ounces. If the conclusion of the test is that the number of ounces of soda in the cans is different from 12.1, the technician will declare that the process is out of control, and the machine will be stopped and calibrated. From previous tests, the technician found that the standard deviation of the number of ounces of soda in the cans is approximately 0.01. The number of ounces of soda in the 10 cans that were tested this week is given below. Assume that the standard deviation from the technician's previous tests is the population standard deviation. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether filling process is out of control and…
Two varieties of lettuce were grown for 16 days in acontrolled environment. The following table shows the totaldry weight (in grams) of the leaves of nine plants of thevariety “Salad Bowl” and six plants of the variety “Bibb.” Compute the standard error of (Y1 - Y2) for these data.
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Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?

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