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Statistics
Chapter 5
20
Mathematics
Undergraduate 2
03/31/2009

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Term
What is a Random Variable
Definition

A variable, usually x, that has a single numerical value, determined by chance, for each outcome of a procedure.

 

Two types: discrete and continuous

Term
What is a Probability Distribution
Definition

a description that gives the probability for each value of the random variable.

It is often in the form of a table, graph, or formula.

Term
What is a Discrete Random Variable
Definition

A discrete random variable is one which may take on only a countable number of distinct values such as 0, 1, 2, 3, 4, ...

 

ex: number of children in a household, cinema attendance, ...

Term
What is a Continuous Random Variable
Definition

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements

ex: height, weight, amount of sugar in an orange, time required to run a mile..

Term

What does the following stand for?

 

ΣP(x) = 1

Definition
The sum of all probabilities must be 1 (where x assumes all possible values)
Term

What does the following stand for?

 

0 P(x)  1

Definition
each prob. value must be between 0 and 1 inclusive (for every individual value of x)
Term
What is the standard deviation formula for 5-2?
Definition

σ = √Σ [(x-µ)2 * P(x)]

 

 

Term
Standard Deviation Range Rule of Thumb
Definition

maximum usual value = μ + 2σ

 

minimum usual value = μ - 2σ

Term
What is the Rare Event Rule?
Definition
If , under a given assumption, the prob. of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
Term
What is Expected Value?
Definition

The expected value of a discrete random variable represents the average value of the outcomes.

It is denoted as E.

 

E = Σ[x * P(x)]

Term
Binomial Prob. Distribution
Definition

1. Fixed number of trials

2. Trials must be independent

3. Outcomes catergorized in 2 ways

4. Prob. of a success remains the same in all trials

Term
What do S, F, p, q, n, x, and P(x) stand for?
Definition

S= success

F= failure

p= prob. of success in one of the n trials

q= prob. of failure in one of the n trials

n= fixed number of trials

x=specific umber of successes in n trials, so x can be any whole number between 0 and 1, inclusive.

P(x)= the prob. of getting exactly x successes amoung the n trials

Term
What does P(S)= p mean?
Definition
The prob. of a success
Term
What does P(F) = 1-p = q mean?
Definition
the prob. of a failure
Term

Are the following formulas for any Discrete Prob. Distribution or Binomial Distributions?

 

μ  = Σ[x*P(x)]

σ2 = Σ[x2 * P(x)] - μ2

σ = √Σ[x2*P(x)] - μ2

Definition
Discrete Prob. Distribution
Term

Are the following formulas used for Discrete Prob. Distributions or Binomial Distributions?

 

μ  = np

σ2 = npq

σ  = √npq

Definition
Binomial Distributions
Term
What is the Poisson Distribution?
Definition

Discrete prob. distribution that applies to occurrences of some event over a specified interval of time, distance, area, volume, or some similar unit.

 

 

Term
What are the variables and formula for Poisson Distribution?
Definition

x is the number of occurrences of the event in an interval.

 

P(x) =  μx * e/ x!

 

where e = 2.71828

Term
What are the four requirements for the Poisson Distribution?
Definition

1. the random variable x is the number of occurrences of an event over some interval

2.the occurrences must be random

3. the occurrences must be independent of each other

4. the occurrences must be uniformly distributed over the interval being used.

Term
What are the parameters of the Poisson Distribution?
Definition

the mean is μ

 

the standard deviation is σ = √μ

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