Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one des...
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one descent?
maybe use induction to prove?
Problem 2: Let p-p.Pn be a permutation considered in its one-line notation. An inversion in p is a pair 1 i<jS n such that j appears to the left of i in p (i.e., an out-of-order pair). Let inv(p) be the total number of inversions in p. Prove that PES where z is a variable.
Problem 2: Let p-p.Pn be a permutation considered in its one-line notation. An inversion in p is a pair 1...
Problem 6. Let P be an n × n permutation matrix with 1's on the anti-diagonal. Find det(P), Hint: How many exchange permutations are needed to implement P?
Problem 6. Let P be an n × n permutation matrix with 1's on the anti-diagonal. Find det(P), Hint: How many exchange permutations are needed to implement P?
(1) Let f : [n] [n] be a permutation. A fixed point of f is an element x e [n] such that f(x) - x. Now consider random permutations of [n] and let X be the random variable which represents the number of fixed points of a given permutation. (a) What is the probability that X 0? (b) What is the probability that X-n -2? (c) What is the probability that X-n-1? (d) What is the expectation of X? (Hint:...
I have to use the following theorems to determine whether or not
it is possible for the given orders to be simple.
Theorem 1: |G|=1 or prime, then it is simple.
Theorem 2: If |G| = (2 times an odd integer), the G is not
simple.
Theorem 3: n is an element of positive integers, n is not prime,
p is prime, and p|n.
If 1 is the only divisor of n that is congruent to 1 (mod p)
then...
Consider the problem of estimating π using a unit square
centered at (1/2, 1/2) and an inscribed circle inside the square.
We will estimate π by simulating n darts. For the nth dart, if the
dart is inside the circle, then we return In = 1; otherwise, we
return In = 0.
1. Are I1, I2, · · · , In independent? Under what
assumption?
2. Are I1, I2, · · · , In identically distributed?
3. Let p represent...
Can any one explain the claim for me please? I cannot see why
thats true as p is greater than 1, surely we will have extra
terms.
To me its like it is calming (a+b)^2 <= a^2 + b^2
Any help will be much appreciated.
Let Take f, g E B: then for any λ E (0, 1) we have CL
Let Take f, g E B: then for any λ E (0, 1) we have CL
all
but dont work on the julia box one which is 2 i think so
1-3-4
Fitchburg State University Department of Mathematics Project #3 Math 2400: Calculus II April 11, 2019 project for Calculus II. You may work on this with up to one other fellow student. Answer all questions completely and type or neatly write out. The final project should be turned in by Tueeday, April 23. How is it that we generate For this project it helps to...
Assume that we have three independent observations: where Xi ~ Binomial(n 7,p) for i E { 1.2.3). The value of p E (0, 1) is not known. When we have observations like this from different, independent ran- dom variables, we can find joint probabilities by multiplying together th ndividual probabilities. For example This should remind you the discussion on statistical independence of random variables that can be found in the course book (see page 22) Answer the following questions a...
Problem 1 N molecules of carbon dioxide gas Co, (considered as an ideal gas) undergo the cycle shown in the P-V diagram on the right. As a reminder, a CO, molecule has all atoms on a line. Assume that all processes are quasistatic and that the temperature remains such that rotational degrees of freedom are activated, but vibrational degrees of freedom are frozen out. Capital letters A, B, C represent the states at the corners of the cycle, while lowercase...