] 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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X={1,2,3,4} find permutations S4=
NS Vol) LTE l 12:10 . b Nancy Just now For n attributes A,, A2, ... , An (A,A2 . An) 2 (A,) + (A2) + ...+ (An) – (n – 1)N Where N is the total number of observations. II II
2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
11 see picture to solve
Q3 Suppose we have two boxes and 2N cards, of which N are blue and N are red. Initially, N of the cards are placed in box 1, and the remainder of the cards are placed in box 2. At each trial a card is chosen at random from each of the boxes, and the two cards are put back in the opposite boxes. Let Xo denote the number of blue cards initially in box 1 and, let Xn for n ≥ 1, be the number of blue cards in box 1 after the nth trial. Find the closed form transition probailities of the Markov chain Xn, n ≥ 0.
An urn contains cards numbered 1.2...100. Let X be the least number on the 50 cards drawn randomly without replacement from the urn. Then P(X2) is
Q.3. Compute the probability that: (a) their sum is odd; (b) their product is even. Three distinct integers are chosen at random from the first 15 positive integers.
Suppose we have a set öf n values! {x1, X2, .., Xn-1, Xn} The sample mean of the above set is x. Prove that if we multiply every value by k, then the new average will be: New average= kã (Hint: Use the formula for the sample mean with the “new" set plugged in, then simplify.)
1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)– P(BnC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC) = 1– P(A^)P(B^)P(C*) = 1– (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 2/5, the probability that B hits it is 5/9, and the probability that C hits the target is 3/7. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p > 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1 — р)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0006 and n = 750, and then round your result to a…

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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?