# Appendix a to applied probability: directory of m-functions and m

 Page 1 / 24
User-defined functions as distinct from the basic MATLAB functions which are part of the MATLAB package. An m-procedure (or sometimes a procedure) is an m-file containing a set of MATLAB commands which carry out a prescribed set of operation

We use the term m-function to designate a user-defined function as distinct from the basic MATLAB functions which are part of the MATLAB package. For example,the m-function minterm produces the specified minterm vector. An m-procedure (or sometimes a procedure ) is an m-file containing a set of MATLAB commands which carry out a prescribed set of operations. Generally, these will prompt for (or assume) certain data upon whichthe procedure is carried out. We use the term m-program to refer to either an m-function or an m-procedure.

In addition to the m-programs there is a collection of m-files with properly formatted data which can be entered into the workspace by calling the file.

Although the m-programs were written for MATLAB version 4.2, they work for versions 5.1, 5.2, and 7.04. The latter versions offer some new features which may make more efficientimplementation of some of the m-programs, and which make possible some new ones. With one exception (so noted), these are not explored in this collection.

## Matlab features

Utilization of MATLAB resources is made possible by a systematic analysis of some features of the basic probability model. In particular, the minterm analysis oflogical (or Boolean) combinations of events and the analysis of the structure of simple random variables with the aid of indicator functions and minterm analysisare exploited.

A number of standard features of MATLAB are utilized extensively. In addition to standard matrix algebra, we use:

1. Array arithmetic. This involves element by element calculations. For example, if `a, b` are matrices of the same size, then `a.*b` is the matrix obtained by multiplying corresponding elements in the two matrices to obtain a new matrix ofthe same size.
2. Relational operations, such as less than, equal, etc. to obtain zero-one matrices with ones at element positions where the conditions are met.
3. Logical operations on zero-one matrices utilizing logical operators and , or , and not , as well as certain related functions such as any , all , not , find , etc. Note . Relational operations and logical operations produce zero-one arrays, called logical arrays , which MATLAB treats differently from zero-one numeric arrays . A rectangular array in which some rows are logical arrays but others are not is treated as a numeric array.Any zero-one rectangular array can be converted to a numeric array (matrix) by the command `A = ones(size(A)).*A` ,
4. Certain MATLAB functions, such as meshgrid, sum, cumsum, prod, cumprod are used repeatedly. The function dot for dot product does not work if either array is a logical array. If one of the pair is numeric, the command C = A*B'will work.

## Auxiliary user-defined building blocks

One of the most useful is a special sorting and consolidation operation implemented in the m-function csort . A standard problem arises when each of a non distinct set of values has an associated probability. To obtain the distribution, it is necessary to sort the values and add the probabilities associated with each distinct value. Thefollowing m-function achieves these operations: function [t,p]= csort(T,P). T and P are matrices with the same number of elements. Values of T are sorted and identical values are consolidated; values of P corresponding to identical values of T are added. A number of derivative functions and procedures utilize csort. The following twoare useful.

```function [t,p] = csort(T,P)% CSORT [t,p] = csort(T,P) Sorts T, consolidates P% Version of 4/6/97 % Modified to work with Versions 4.2 and 5.1, 5.2% T and P matrices with the same number of elements % The vector T(:)' is sorted:% * Identical values in T are consolidated; % * Corresponding values in P are added.T = T(:)'; n = length(T);[TS,I] = sort(T);d = find([1,TS(2:n) - TS(1:n-1)>1e-13]); % Determines distinct valuest = TS(d); % Selects the distinct values m = length(t) + 1;P = P(I); % Arranges elements of P F = [0 cumsum(P(:)')]; Fd = F([d length(F)]); % Cumulative sums for distinct values p = Fd(2:m) - Fd(1:m-1); % Separates the sums for these values```

what is economic integration
why does it makes sense to let the sewage disposal company in your town have a monopoly?
how might a monopoly affect price?
Janice
how might a monopoly affect prices?
Janice
The principle of Economic is one to be involved in any economic buying substance
reason of corporation
Mohamed
What is economic integration
Mohamed
what are the principle of economics?
What is (Qs)
What is (Qs) and (Qd)
Bigi
Quantity of supply and Quantity of demand
Dilshoda
Qs: Is quantity of supply and Qd: quantity of demand
Cabdikariim
give as me quantitys
ahmed
among all the definition of economics which of the definition is generally acceptable?
oche
i science that studies human behavior as a relationship between ends and scarcity that have alternative uses
ousman
okay......
oche
what are the principle of economics?
oche
what Make things scarce
why do we studied economic
Soudani
for the stability and growth of any reign.
Fayaz
what is macro economics.?
Fayaz
which part of economics is interesting..
Fayaz
what is economic integration
Mohamed
how does economics define me
what are the factors that determines the demand and supply
sillah
what are the importance of Economics
tell me something very important about economics..
how may I solve arithmetic mean ,,,all example
what is agriculture
simple method of understanding cost concept
what is inflation
Inflation is a general increase in price levels
Zuko
is the action of inflating something
Abdifatah
inflation is the persistent increase in general price level of goods and services in an economy over a considerable period of time .
Tetteh
inflation is the general increase of a commodity in a particular period of time.
Turay
inflation is a general increase in price levels of commodities
shehu
what are the types of inflation?
Ebrima
inflation is the period of persistent rise in the general level of the price of goods services over time
Emmanuel
we have creeping inflation, demand pull inflation ,cost push inflation, and galloping inflation .
Emmanuel
I s Nigeria in any kind of in inflation? If yes which kind?
Martins
please can someone help me with the principles of economic?
Jonathan
and u
ahmed
no discassion just question
Aliraza
what is science and art economic
how can a location of a firm create difference between producers
what is monetary policy
joy
hello
Abdifatah
is a monetary from policy that's authorized of country encharces
Abdifatah
What would you say about the the mobility of enterprise as a factor of production?
Difference between extinct and extici spicies
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive