Question

a) What is an exponential distribution (include an APA citation)? ___________________________

b) When would you use an exponential distribution? ________________________

c) What is a binomial distribution (include an APA citation)?_______________________

d) When would you use a binomial distribution? ___________________

3. Task

Run these commands in R, then use your own words to describe what the resulting numbers represent.  You can get some information about the functions by using the help commands in R (such as ?pbinom to get information about the pbinom() command in R):

a) pbinom(q=5, size=10, prob=1/6)

b)

n=10
p=.5
x=9
pbinom(x, n, p)

c) punif(5, min=1, max=10) - punif(4, min=1, max=10)

Answer 1

Solution:

In pobability theory and statistics,the exponential distribution is the probability distribution that describes the time between events in a poisson process,i. a process in which events occur continuously and independently at a constant average rate.It is a particular case of the gamma distribution.It is the continuous analogue of the geometric distribution,and it has the key property of being memoryless.In addition to being used for the analysis of poisson processes,it is found in various other contexts.

The probability density function (pdf) of an experimental distribution is

f(x;) ={e^-x x 0,

0 x0.

Now use the exponential distribution to model poisson processes,in which events occur continuously and independently at a constant rate.

b) When would you use an exponential distribution?

ans) This distribution has a wide range of applications,queuing theory,Morkav chains and including reliability products and systems.

now for example,the exponential distribution can be used to model:

How long it takes for electronic components to fail

.Service time interval between customer's arrivals at a terminal

.The time until default on a paymnt(credit risk modlimng)

.The time interval between customer's arrivals at a reminal

.The distance betwen mutations on a DNA strand

c)What is a binomial distribution(include an APA citation)?

ans) from Binomial Experiment

A Binomial Experiment has the following properties:

. The probability of success,denoted by p1 whichis the same on every trial.

. The experiment consist of n repeated trials.

.Eachn trial can results in two just posible outcomes.we call one of thse outcomes a success and the other,a failure.

Now to consider the following statistical experiment.

You flip a coin 2 times and count the number of times the coin on heads.So this is a binomial experiment because:

.The experiment consists of repeated trials.we flip a coin 2 times.

The probability of success in constant -0.5 every trial.

.Here each trial can result in just two possilble outcomes-heads or trialsere the trials are independent;that is heads on one trial does not affect whether we get heads on other trials.

Binomial Formula:

Suppose a binomial experiment consists of n trials and results in x successes,so if the probability of success on an individual trial is p1, then the probability is:

b(x,n,p)=nCx*P*(1-P)^n-x

d) When would tyou use a binomial distribution?

ans)the probabality distribution of n independent trials are conducted and we want to find the probability of r success,each success has probability p of occuring.The definition boils down these below 4 conditions:

1)Independent trials

2)Two different classifications

3)Fixed number of trials

4)Probability of success stays the same for all trials

Here all of these must be present in the process under investigation in order to use the binomial probability formula (or) tables.

now Run these commands in R,then use your own words to describe what the resulting numbers represent.

You can get some information about the fuctions by using the hlp commands in R

>pbinom(q=5,size=10,prob=1/6)

[1]0.9975618