Prove that for two machines M and N, M indistinguishable from N does not imply that M has the same behavior as N. Hint: one way to prove this is to exhibit two machines, a two state machine M and a three state machine N, both over X = {0,1} and Y = {0,1} with this property
Prove that for two machines M and N, M indistinguishable from N does not imply that...
Two machines produce metal parts. The mean of the weight of these parts is of interest. The following data have been collected Machine 1 N 30 x(dash) = 0.984 σ 3.67 Machine 2 n 35 x (dash) 0.907 σ 3.11 a. Do both machines produce parts with a statistical same mean weight? State your null and alternative hypothesis, and use a 1% level of significance. b. If we want the confidence interval to have a half width of 0.05, how...
In a restaurant there are three machines frying chips. At any given moment, at least two of the three machines are working. Otherwise a "STOP" sign must be hung on the machines and it will have to get repaired. Define Yi as the life span of the i-th machine that is distributed as Gamma (3,1) (in the months). Suppose that the machines work independently of each other. 1) Find the density function of Yi. What is the probability that one...
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A company utilices two different machines to manvufacture parts of a certain type. During a single shift, a sample of n -20 parts produced by each machine is obtained, and the value of a particadar critical dimension for each part is determined. The side by side boxplot below is constructed from the resulting data. Machine Dimenn 85 93 105 115 Compare and contrast the two samples.(Hint: Three are correct.) (Select all that apply.) The only outlier that exists...
New problems for 2020 1. A topological space is called a T3.space if it is a T, space and for every pair («,F), where € X and F(carefull), there is a continuous function 9 :X (0,1 such that f(x) 0 and f =1 on F. Prove that such a space has the Hausdorff Separation Property. (Hint: One point subsets are closed.] 2. Let X be topological space, and assume that both V and W are subbases for the topology. Show...
(a) (1) Draw a PDA for the language {01'01moin+m | n, m1} (2) Does your PDA use non-determinism? (3) Include a brief description of how it operates. (b) Answer the same three questions for the language of palindromes over the alphabet ={0,1}
Q4: 3 marks A manufacturer has three machines I, Il and Il installed in his factory. Machines I and Il are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machines are...
a be a real number . If a--a, prove that either a 0 or a 1. 8. (Pigeonhole Principle) Suppose we place m pigeons in n pigeonholes, where m and n are positive integers. If m > n, show that at least two pigeons must be placed in the same pigeonhole. [Hint (from Robert Lindahl of Morehead State University): For i 1, 2, . . . , n, let Xi denote the number of pigeons that are placed in the...
1. Suppose a and b are elements of a group G. Prove, by induction, (bab−1)n = banb−1 . Hence prove that if a has order m, then bab−1 also has order m. Deduce from question (#1) that in any group ab and ba have the same order (you may assume ab has finite order). The assertion in Question (#1) can be generalized to an assertion about isomorphisms. State and prove it.
4. A company manufactures two products, X and Y by using three machines A, B, and c Each of the products has to be processed on each machines. The Table below shows (a) the hours required on each machine to produce one unit of each of the products (b) the total number of hours available on each machine (c) the profit made on one unit of each product. It is assumed that the profit is directly proportional to the number...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...