# 7.1 Distribution approximations  (Page 2/3)

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Use of m-procedures to compare

We have two m-procedures to make the comparisons. First, we consider approximation of the

Poisson $\left(\mu \right)$ distribution. The m-procedure poissapp calls for a value of μ , selects a suitable range about $k=\mu$ and plots the distribution function for the Poisson distribution (stairs) and the normal (gaussian) distribution (dash dot) for $N\left(\mu ,\mu \right)$ . In addition, the continuity correction is applied to the gaussian distribution at integer values (circles). [link] shows plots for $\mu =10$ . It is clear that the continuity correction provides a much better approximation. The plots in [link] are for $\mu =100$ . Here the continuity correction provides the better approximation, but not by as much as for the smaller μ .

The m-procedure bincomp compares the binomial, gaussian, and Poisson distributions. It calls for values of n and p , selects suitable k values, and plots the distribution function for the binomial, a continuous approximation to the distribution function for the Poisson,and continuity adjusted values of the gaussian distribution function at the integer values. [link] shows plots for $n=1000$ , $p=0.03$ . The good agreement of all three distribution functions is evident. [link] shows plots for $n=50$ , $p=0.6$ . There is still good agreement of the binomial and adjusted gaussian. However, the Poisson distribution does nottrack very well. The difficulty, as we see in the unit Variance , is the difference in variances— $npq$ for the binomial as compared with $np$ for the Poisson.

## Approximation of a real random variable by simple random variables

Simple random variables play a significant role, both in theory and applications. In the unit Random Variables , we show how a simple random variable is determined by the set of points on the real line representingthe possible values and the corresponding set of probabilities that each of these values is taken on. This describes the distribution of the random variable and makes possible calculations of eventprobabilities and parameters for the distribution.

A continuous random variable is characterized by a set of possible values spread continuously over an interval or collection of intervals. In this case, the probability is also spread smoothly. The distributionis described by a probability density function, whose value at any point indicates "the probability per unit length" near the point. A simple approximation is obtained by subdividing an interval whichincludes the range (the set of possible values) into small enough subintervals that the density is approximately constant over each subinterval. A point in each subinterval is selected and is assigned the probabilitymass in its subinterval. The combination of the selected points and the corresponding probabilities describes the distribution of an approximating simple random variable. Calculations based on thisdistribution approximate corresponding calculations on the continuous distribution.

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Rafiq
what is differents between GO and RGO?
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive