Prove that the number of unordered sequences of length k with elements from a set X...
Prove that the number of unordered sequences of length k with elements from a set X of size n is n+k−1 k . Hint: For illustration, first consider the example n = 4, k = 6. Let the 4 elements of the set X be denoted a, b, c, d. Argue that any unordered sequence of size 6 consisting of elements a, b, c, d can be represented uniquely by a symbol similar to “··|·|··|·”, corresponding to the sequence aabccd. Now count the number of choices for the vertical bars
Homework Answers
Prove the number of unordered number of sequence of length k
eliments from a set of size n i.e (n+k-1 k) 
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Prove that the number of unordered sequences of length k with
elements from a set X...
PLEASE DO BOTH (5) (5 pts) Prove the identity (1) () = (x) (---), whenever n,...
PLEASE DO BOTH
(5) (5 pts) Prove the identity (1) () = (x) (---), whenever n, r, and k are non-negative integers with rn andk Sr. (6) (5 pts) How many ways are there to select five unordered elements from a set with three elements when repetition is allowed?
Please prove Theorem 7.20: Let (X, T) be a topological space. Then the following are all topological properties the number of elements in X, the number of T-open sets, and having a T-open set contain...
Please prove
Theorem 7.20: Let (X, T) be a topological space. Then the following are all topological properties the number of elements in X, the number of T-open sets, and having a T-open set containing n elements (for any natural number n
Theorem 7.20: Let (X, T) be a topological space. Then the following are all topological properties the number of elements in X, the number of T-open sets, and having a T-open set containing n elements (for any natural...
A 13. Let X be a p-element set and let Y be a k-element set. Prove that the number of functions f :X >Y which map X...
A 13. Let X be a p-element set and let Y be a k-element set. Prove that the number of functions f :X >Y which map X onto Y equals k!S(p, k) S#(p, k) :
A 13. Let X be a p-element set and let Y be a k-element set. Prove that the number of functions f :X >Y which map X onto Y equals k!S(p, k) S#(p, k) :
Problem 7. (20 pts) Let n N be a natural number and X a finite set...
Problem 7. (20 pts) Let n N be a natural number and X a finite set with n elements. Show that the number of permutations of X such that no element stays in the same position is n. n! k! For instance, there are 6-3! permutations of 3 elements, but only 2 of them are permutations which fix no element. Similarly, there are 24 41 permutations of 4 elements, but only 9 which fix no element Hint: Use the Inclusion-Erclusion...
Question 1) Suppose a program has the following code: const int X = 2, Y =...
Question 1) Suppose a program has the following code: const int X = 2, Y = 3; int sum; int values[X][Y] = {{1, 2, 3}, {4, 5, 6}}; for(int i=0; i<X; i++) { sum=0; for(int j=0; j<Y; j++) sum+=values[i][j]; cout<<sum<<endl; } What is this program getting the sum of? Group of answer choices D-) The columns of the 2D array C-) The rows of the 2D array A-) All of the elements of the 2D...
I need to prove bimultivariate below equation follow chi-square degree of freedom number2 at the sample meun vector and sample covariance matri omesponding popolation quantities; that is /(X)-...
I need to prove bimultivariate below equation follow
chi-square degree of freedom number2
at the sample meun vector and sample covariance matri omesponding popolation quantities; that is /(X)-μ and E(S)-z 514 Chapher 11Multivariate SP We can show th ndcontrolprocedure is the Hot It is a direct analog of the the Hotelling T 11.3 The Hotelling Control Chart The most familiar multivariate process-monitoringa control chart for monitoring the mean vectoro variate Shewhart i chart. We present two versions grouped data, and...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system ...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...
and w Two-dimensional gel electrophoresis separates proteins based on a. shape; charge Ob.size; concentration c. concentration;...
and w Two-dimensional gel electrophoresis separates proteins based on a. shape; charge Ob.size; concentration c. concentration; shape O d. size, charge O e. size; shape Refer to the table. Several strains of a bacterium are sequenced to investigate the pan and core genomes. In the table, + denotes presence of the gene and denotes its absence. Gene Gene Gene Gene Gene Strain ! Strain 2 + Strain 3 + Strain 4 + + + + Strain 5 + + What...
Assignment Predator / Prey Objectives Reading from and writing to text files Implementing mathematical formulas in...
Assignment Predator / Prey Objectives Reading from and writing to text files Implementing mathematical formulas in C++ Implementing classes Using vectors Using command line arguments Modifying previously written code Tasks For this project, you will implement a simulation for predicting the future populations for a group of animals that we’ll call prey and their predators. Given the rate at which prey births exceed natural deaths, the rate of predation, the rate at which predator deaths exceeds births without a food...
Use the C programming language to complete #include <stdio.h> #include <stdlib.h> #include <float.h> // Declare Global...
Use the C programming language to complete
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
// Declare Global variables here.
void array_stats() {
// Insert your solution here.
}
#include <stdlib.h>
#include <time.h>
int main() {
// Simulate the test setup process.
srand( time( NULL ) );
for ( int i = 0; i < 32; i++ ) {
val[i] = rand();
}
val_count = rand();
val_mean = rand();
val_min = rand();
val_max = rand();
// Call submitted code.
array_stats();
// Display...
PLEASE DO BOTH
(5) (5 pts) Prove the identity (1) () = (x) (---), whenever n, r, and k are non-negative integers with rn andk Sr. (6) (5 pts) How many ways are there to select five unordered elements from a set with three elements when repetition is allowed?
Please prove
Theorem 7.20: Let (X, T) be a topological space. Then the following are all topological properties the number of elements in X, the number of T-open sets, and having a T-open set containing n elements (for any natural number n
Theorem 7.20: Let (X, T) be a topological space. Then the following are all topological properties the number of elements in X, the number of T-open sets, and having a T-open set containing n elements (for any natural...
A 13. Let X be a p-element set and let Y be a k-element set. Prove that the number of functions f :X >Y which map X onto Y equals k!S(p, k) S#(p, k) :
A 13. Let X be a p-element set and let Y be a k-element set. Prove that the number of functions f :X >Y which map X onto Y equals k!S(p, k) S#(p, k) :
Problem 7. (20 pts) Let n N be a natural number and X a finite set with n elements. Show that the number of permutations of X such that no element stays in the same position is n. n! k! For instance, there are 6-3! permutations of 3 elements, but only 2 of them are permutations which fix no element. Similarly, there are 24 41 permutations of 4 elements, but only 9 which fix no element Hint: Use the Inclusion-Erclusion...
I need to prove bimultivariate below equation follow
chi-square degree of freedom number2
at the sample meun vector and sample covariance matri omesponding popolation quantities; that is /(X)-μ and E(S)-z 514 Chapher 11Multivariate SP We can show th ndcontrolprocedure is the Hot It is a direct analog of the the Hotelling T 11.3 The Hotelling Control Chart The most familiar multivariate process-monitoringa control chart for monitoring the mean vectoro variate Shewhart i chart. We present two versions grouped data, and...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...
and w Two-dimensional gel electrophoresis separates proteins based on a. shape; charge Ob.size; concentration c. concentration; shape O d. size, charge O e. size; shape Refer to the table. Several strains of a bacterium are sequenced to investigate the pan and core genomes. In the table, + denotes presence of the gene and denotes its absence. Gene Gene Gene Gene Gene Strain ! Strain 2 + Strain 3 + Strain 4 + + + + Strain 5 + + What...
Use the C programming language to complete
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
// Declare Global variables here.
void array_stats() {
// Insert your solution here.
}
#include <stdlib.h>
#include <time.h>
int main() {
// Simulate the test setup process.
srand( time( NULL ) );
for ( int i = 0; i < 32; i++ ) {
val[i] = rand();
}
val_count = rand();
val_mean = rand();
val_min = rand();
val_max = rand();
// Call submitted code.
array_stats();
// Display...
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