We'll say that a permutation T = (T(1),..., T(n)) contains a swap if there exist i, j E {1,.,n} sothat T(i) = j and A(j) =i, where i + j... .(a) What is the expected number of swaps in a random permutation?(b) What about the variance?(c) In the same spirit as above, we'll say that T contains a s-cycle if there exist i1,..., is E {1,...,n}with T (i1) = i2, T (i2) = i3,..., T(i,) =i1. Compute the expectation of the number of s-cycles.•...

a) Let we take n > 1. Let Xi be a random variable if i is a partner in a swap or not. The values…

Answered: We’ll say that a permutation T =…

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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show that if X11, X12,..., X1, X21, X22,..., X2n₂ are independent random variables, with the first n constitut- ing a random sample from an infinite population with the mean μ₁ and the variance of and the other n2 constitut- ing a random sample from an infinite population with the mean μ2 and the variance o2, then 1 M2 (a) E(X₁-X₂) = μ₁ −μ2; 07 0 22 (b) var(X₁-X₂) = + n₁ n₂
1. The random variables §, §1, §2,... are independent and identically distributed with 1/4 and P(§ = j) = c/j for j = 1,2,3. Let X₁ = 0 and Xn = max(§₁, ..., Èn) for n = 1, 2,.... distribution P(§ = 0) = (a) What value must c take? (b) Explain why {Xn, n = 0, 1, 2,...} is a Markov chain. (c) Write down the transition matrix. (d) Draw the transition diagram and classify the states (aperiodic, transient, re- current, eorgodic, etc). (e) Calculate P(Xn = 0). (f) Calculate P(X₁ = 3, X₂ = 1|X₁ = 3).
A docs.google.com/forms/d/e (1) Let X be a random variable with p.d.f. fx) =- , then O.w (b) k- (0) k = (a) k=1 (d) k-5 (e) None of these a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer (2) Let X be a random variable with a function x= 0,1, 2,3 4 x! (3-x)! f(x) = , then p(x<1) is 0.w (b) (d) (e) None of these 27 (a) 27 (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer
Suppose P and Q are two independent events with P(P) = 0.23, P(P and Q)= 0.18 Calculate P(Q)
2. Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia P STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2: Here needs justification By Cauchy Schwarz inequality it can be shown that the right hand side is always positive. Analogs expression in Mechanic : Parallel axis theorem Iem = I– md² Moment of Moment of inetria about Inertia of an an axis shifted object about the center of a mass by d from center of mass (a parallel shift) Icm is dispersion around the mean and is like second central moment (variance) I is like second moment if d is mean m is like sum total all the weight of each of the x which all add up to 1 d squared is like squared of mean since we,
A box has 3white(W) balls,2 black (B) balls and 4 red(R) balls. Two balls were drawn successively from this box (i) with replacement/ (ii) without replacement. Let X=the number of white balls drawn and let Y=the number of black balls drawn.
(2) Let X be a random variable with p.d.f. ke S(x) ={ *>x>0 , then O.w (a) k-4 (0) k- (d) k-3 (e) None of these (b) k-7 a is the correct answer bis the correct answer c is the correct answer d is the correct answer e is the correct answer
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.
(1) Let X be a random variable with p.d.f. ke 3 0
Suppose that events E and F are independent with P(E) = 0.5 and P(F)=0.9 What is P(E and F)
Assume A and B are independent events with P(A) = 0.14 and P(B) = 0.55. Find (a) P(A N B), (b) P(A U B), (c) P (A'n B'), (d) P (A' N B), and (e) P (ANB'). ..... (a) P(A N B) = (Type an integer or a decimal.) (b) P(A U B) = (Type an integer or a decimal.) (c) P (A' n B') = (Type an integer or a decimal.) (d) P (A'N B) = (Type an integer or a decimal.) (e) P (AN B') = (Type an integer or a decimal.)

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