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Math Project

Data Management In Real Life
by

Zhang Ken

on 1 March 2013

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Transcript of Math Project

Ken, it's Janice! I love your new background!
:DDDD
Anyway, your idea about increasing tax is good but how much?
and, you said we need to learn about our career, but did you know in grade 10 we had a class called career and civic?

That class is basically talking about career! Application of Binomial Distribution in Traffic Flaw Poisson and Binomial Distributions in Traffic Flow By Yanjun Luo, Yukang Zhang, Janice Lin and Kate Azizova Application in the traffic flow Poisson vs Binomial For conditions in which the Poisson distribution applies-i.e., under conditions of "free flow"-it is possible to compute the probability of o, i, 2 . . . . . . . .k vehicles arriving per time interval of t seconds provided the hourly volume, V, is known:
t = length of time interval in seconds
V = hourly volume
n = number of intervals (per hour) = 36oo/t
m = average number of vehicles per interval
= V/3600/t = Vt/3600 Then the probability, P(x), that x vehicles will arrive during any interval is:





The hourly frequency, F, of intervals containing x vehicles is: Example 1 PREDICTION OF ARRIVALS (Low Volume) The Poisson distribution: A discrete distribution. It is often used as a model for the number of events
in a specific time period.
The Binomial Distribution: It's a discrete distribution. All the trials are independent and have only two possible outcomes, success or failure. The probability of success is the same in every trial- the outcome of one trail does not affect the probabilities of any of the later trails. The random variable is the number of successes in a given number of trails. 1. The major difference between Poisson and Binomial distribution is that the Poisson does not have a fixed number of trials. Instead, it uses the fixed interval of time or space in which the number of successes is recorded.
2. Another difference is that for binomial distribution, the outcome of one trail does not affect the outcomes of other trails. But for Poisson distribution, it depends...
3. One similarity is that both of them are discrete distributions. Discrete variables have values that are separate from each other. Good morning!
Welcome to our
presentation DO YOU KNOW..

What is Poisson distribution?

DO YOU KNOW....
How to find the number of traffic accidents that occur on a particular stretch of road using Poisson distribution?

DO YOU KNOW...

What are the differences between Poisson and Binomial? The Poisson Distribution Poisson distribution is a discrete distribution that expresses the probability of a given number of events occurring in a fixed interval of time with only one variable. Well it is often used as a model for the number of events in a specific time period such as distance, area or volume. The Formula is:

The formula means suppose that we can expect some independent event to occur " " times over a specified time interval. The probability of exactly "x" occurrences will be equal to
P (x; ) = Binomial distribution is mainly used to:
It can simulate the arrival of turning vehicles
calculate the accident frequency happens in a specific intersection Condition:
This distribution can only be used when an event has two outcomes.
The probability of one outcome must have a higher chance than 1%. Back to his history..... Bonjour a tous!
My name is Simeon Denis Poisson
I am a French mathematician and i developed this distribution in 1837.
This distribution was occupied just a single page of a paper entitled "Researches on the probability of criminal and civil verdicts". The work focused on certain random variables N that count, among other things, the number of discrete occurrences (sometimes called “arrivals”) that take place during a time-interval of given length.
In this paper, I looked at the form of the binomial distribution when the number of trials was large then i got the cumulative Poisson distribution as the limiting case of the binomial, when the probability of a success tends to zero Application of Binomial Distribution in Traffic Flaw λ how to solve the right or left turn question:

There is 100 vehicles in total turn left of right in a intersection. A vehicle has a 40% chance turns left. What is the probability that 34 vehicles turn right in the intersection?


P(34)=100C34×(0.4)^34×(0.6)^(100-34) More definitions: another left, right turn example: Base of the natural log
e = 2.71828... An average rate of value Poisson random variable The positive real number λ is equal to the expected value of X and also to its variance

The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. The Poisson distribution is sometimes called a Poissonian Relationship between Poisson and Binomial distributions ---







As a rule, N should be at least 50, and p is less than 0.01 The Poisson distribution is based on 4 assumptions:

We use the term "interval" to refer to the context of the problem
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1. The probability of observing a single event over a small interval is approximately proportional to the size of that interval

2. The probability of two events occurring in the same narrow interval is negligible

3. The probability of an event within a certain interval does not change over different intervals

4. The probability of an event in one interval is independent of the probability of an event in any other non-overlapping interval Ken, talk to Brenda that her part is just the same as Jedis
They all talk about lack of future planning....

Brenda should think of another one!!!!!!!!!!!! Ken when i was uploading my ppt to you, i can not receive you email....
Full transcript