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

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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 the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
Difference between extinct and extici spicies
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive      By    By Mistry Bhavesh