] Let A be a set of n 2 2 distinct mumbers and let ajaz. a, be a permutation of A.For i = 2,3, ...,n we say that position i in the permutation is a step if a,-1 < qj. We also go5. [ahead and just consider position 1 a step. What is the expected number of steps in a randompermutation of A?

The statistics of random permutations such as the cycle structure of a random permutation are of…

Answered: 5. [ ] Let A be a set of n 2 2 distinct…

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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. The probability that two specified letters will be placed in the correct envelopes is 1[n(n – 1)]. The probability that none of the othern – 2 letters will then be placed in the correct envelopes is qn-2. Therefore, the probability that only the two specified letters, and no other letters, will be placed in the correct envelopes is 1 -¶n-2. It follows that the probability that exactly two of the n п(п — 1) letters will be placed in the correct envelopes, without specifying which pair will be correctly placed,
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FaE (ax:blb) Compute the followng probabilities 1)+n.b 1) n-ax+nb 11) n(a+b) V) niatx NAHSHAL4 fris distributedN(4,9), P. (Ys6) = If Y is distributed N (-3,4), Pr (Y>-1)- ICN is distributed N(50,25), Pr (43 YS 54) = 4 deemalplaces
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there are no pairs of consecutive integers in the winning combination (i1,..., ix) if and only if (j1, ..., jk) has no repeats. The total number of winning combinations is In part k (c), we computed the number of winning combinations with no repeats among (j1,.. ,jk) to be n – k+1 So, the probability of no consecutive integers is k
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5. [ ] Let A be a set of n 2 2 distinct mumbers and let aja an be a permutation of A. For i = 2,3,...n we say that position i in the permutation is a step if a,-I < qj. We also go ahead and just consider position l a step. What is the expected number of steps in a random permutation of A?