# Appendix a to applied probability: directory of m-functions and m  (Page 12/24)

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## Binomial, poisson, and gaussian dstributions

bincomp.m Graphical comparison of the binomial, Poisson, and Gaussian distributions. The procedure calls for binomial parameters $n,p$ , determines a reasonable range of evaluation points and plots on the same graph the binomial distribution function, thePoisson distribution function, and the gaussian distribution function with the adjustment called the “continuity correction.”

% BINCOMP file bincomp.m Approx of binomial by Poisson and gaussian % Version of 5/24/96% Gaussian adjusted for "continuity correction" % Plots distribution functions for specified parameters n, pn = input('Enter the parameter n '); p = input('Enter the parameter p ');a = floor(n*p-2*sqrt(n*p)); a = max(a,1); % Prevents zero or negative indicesb = floor(n*p+2*sqrt(n*p)); k = a:b;Fb = cumsum(ibinom(n,p,0:n)); % Binomial distribution function Fp = cumsum(ipoisson(n*p,0:n)); % Poisson distribution functionFg = gaussian(n*p,n*p*(1 - p),k+0.5); % Gaussian distribution function stairs(k,Fb(k+1)) % Plotting detailshold on plot(k,Fp(k+1),'-.',k,Fg,'o')hold off xlabel('t values') % Graph labeling detailsylabel('Distribution function') title('Approximation of Binomial by Poisson and Gaussian')grid legend('Binomial','Poisson','Adjusted Gaussian')disp('See Figure for results')

poissapp.m Graphical comparison of the Poisson and Gaussian distributions. The procedure calls for a value of the Poisson parameter mu, then calculates and plots the Poissondistribution function, the Gaussian distribution function, and the adjusted Gaussian distribution function.

% POISSAPP file poissapp.m Comparison of Poisson and gaussian % Version of 5/24/96% Plots distribution functions for specified parameter mu mu = input('Enter the parameter mu ');n = floor(1.5*mu); k = floor(mu-2*sqrt(mu)):floor(mu+2*sqrt(mu));FP = cumsum(ipoisson(mu,0:n)); FG = gaussian(mu,mu,k);FC = gaussian(mu,mu,k-0.5); stairs(k,FP(k))hold on plot(k,FG,'-.',k,FC,'o')hold off gridxlabel('t values') ylabel('Distribution function')title('Gaussian Approximation to Poisson Distribution') legend('Poisson','Gaussian','Adjusted Gaussian')disp('See Figure for results')

## Setup for simple random variables

If a simple random variable X is in canonical form, the distribution consists of the coefficients of the indicator funtions (the values of X ) and the probabilities of the corresponding events. If X is in a primitive form other than canonical, the csort operation is applied to the coefficients of the indicator functions and the probabilities of the corresponding events to obtainthe distribution. If $Z=g\left(X\right)$ and X is in a primitive form, then the value of Z on the event in the partition associated with t i is $g\left({t}_{i}\right)$ . The distribution for Z is obtained by applying csort to the $g\left({t}_{i}\right)$ and the p i . Similarly, if $Z=g\left(X,Y\right)$ and the joint distribution is available, the value $g\left({t}_{i},{u}_{j}\right)$ is associated with $P\left(X={t}_{i},Y={u}_{j}\right)$ . The distribution for Z is obtained by applying csort to the matrix of values and the corresponding matrix of probabilities.

#### Questions & Answers

why is economics important
What will you do as a consumer if you are not at equilibrium?
am new I will like to know about the graph relationship
comment on WTO principle on trading system. trade without discrimination
optimize z=f(x,y)=6x²-9x-3xy-7y+5y²
What is an indifference curve?
different levels of utilities of a person in a given set of bundles of goods
RAM
identify and quantify five social costs and social benefits of building a school
identify and quantity five social costs and social benefits of building a hospital
Mokgobo
short run vs long run
Jean
state the law of diminishing return?
Ibrahim
The Law of Diminishing (Marginal) Returns simply states that at some point in time a business/operation/etc.'s increased productivity will begin to decline.
The
For example, if a small pizza shop currently has 3 workers in the kitchen at any given time,and hiring 1 more worker will increase productivity, at some number of workers hired will the business see a decrease in productivity because the capital resources that the pizza shop has is not infinite.
The
Five social benefits of building a hospital, in my opinion and depending on where it's built, would be 1) Increased care for neighboring residents, 2) Potential jobs for individuals, 3) May decrease the travel time residents need to endure in order to reach the nearest hospital
The
4) May create work-study programs for individuals who aspire to be future Doctors, Nurses, Physicians, etc. 5) Assuming there are local pharmaceutical businesses nearby, the hospital may decide to purchase supplies local, increasing the business' sales. Thus, generating more income.
The
5 costs of building a hospital would be 1) Increased noise and waste pollution from service vehicles and hospital visitors, 2) May require large amounts of space, possibly jeopardizing nearby animal habitats, 3) May see an increase in traffic and possibly car accidents from frantic individuals
The
racing to see their injured friends, family members, etc. 4) Constructing a hospital and hiring staff is very expensive 5) To use funds, private or public, to finance the construction of a hospital cannot be used to fund any other projects. (The concept of opportunity costs.)
The
what is meant by inteference with the price mechanism operation?
Mugen
We use a Supply and Demand graph to illustrate at what price level will the market for a certain good or service be at equilibrium. If the price for a good or service is set too high, consumers will be less inclined to buy that product Thus, creating a surplus.
The
This surplus will eventually drive the price back down to it's equilibrium point. Similarly, if a price for a good or service is set too low, individuals would be more inclined to buy more of a certain product, creating a shortage. This shortage will cause sellers to drive the price back up to the
The
equilibrium point.
The
is it true that the opportunity cost of unemployed labour is zero?
no
Oigebe
give two forms of collusion
1.Explicit Collusion: Also termed overt collusion, this occurs when two or more firms in the same industry formally agree to control the market .
Gafar
2.Implicit Collusion: Also termed tacit collusion, this occurs when two or more firms in the same industry informally agree to control the market, often through nothing more than interdependent actions. A prime example of implicit collusion is price leadership .
Gafar
explicit collusion: this occurs when two or more firms in the same industry legally agree to control the market
Panashe
implicit collusion this occurs when two or more firms in the same industry illegally agree to control the market
Panashe
what is responsible for investigating cases of collusion
nondumiso
what mean economic as a science
Godwin
reasons why a country maybe involved in international trade
state five similarities and differences between money market and capital market
Give a Zimbabwean example of firms operating in an oligopoly market and illustrate using diagrams how a manager in such a market maximize profit
what is an industry
An industry is the production of goods and related services within an economy
Prabhu
an industry is place where goods and services are produced for human consumption....
Usman
scarcity is the major course of economics problems. discuss
please say about that it is interesting for us
Abayneh
what is economics
economics is a social sciences that deals with the production distribution and consumption of goods and services produced.its study of behaviour between economic agents
rkesh
what is the formula for elasticity of demand
Ridwan
change in demand/change in variable variable may be price, income,
rkesh
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
A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive