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Solution:

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3. Let P be a transition matrix of an irreducible Markov chain with n states. Prove that for each two states iメj there exists k-n-1 such that P > 0.
3. Let P be a transition matrix of an irreducible Markov chain with n states. Prove that for each two states iメj there exists k-n-1 such that P > 0.
*Please write or type clearly with explanation for a quick thumbs up: Use mathematical induction to prove that n(n+5) is divisible by 2 for any positive integer n.
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uicuiate the electric force that acts on each ion. THE ELECTRIC FIELD .A point charge of 4.0 puC is a: the origin. What are the 37 magnitude and direction of the electric field on the x axis at (a) = 6.0 m and (b) x =-10 m? (c) Sketch...
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7. Prove that every stochastic process {Xy): t=0.1, } with independent increments is a Markov process. (Remark: This is not true of stochastic processes
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3. The circumference of a sphere was measured to be 84 cm with a possible error of .5 cm. Use differentials to estimate the maximum error in the calculated volume. Then find the relative error (C = 27r; V= #r3, relative error "Y). You may leave the maximum error in terms of 3 TT.
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The combination of these two carbonyl systems can give an aldol product. Part 1. Will more than one enolate form? Part 2. What kind of base would you use? (NaOH or LDA) Why? Part 3. If you were in the lab running this experiment, which reagent (2,2-dimethylpropanal or phenylacetaldehyde) should you add slowly to...
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6. a. Prove that there is a finite field E with 729 elements and provide the quotient ring that is isomorphic to E. b. Draw the lattice of subfields for E.
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Find the LU decomposition of the matrix. 25 5 4 10 8 16 8 12 22
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4. (a) let x[n] be a finite duration signal of duration N. Let y[n] = DFT(DFT(a[n])). All DFTs are N point DFTs. Find vinl in termas of rinl Prove all the properties you use in arriving at your result (b) Let an] and yIn] be sequences of duration N with...
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SHORT ANSWER #29: How would you carry out the synthesis below? Show the reagents needed for each step of your transformation, but do NOT draw the mechanisms for each step. (10 points) NH2 N