Continuous Distributions F10

Continuous Distributions F10 - CONTINUOUS PROBABILITY...

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CONTINUOUS PROBABILITY CONTINUOUS PROBABILITY DISTRIBUTIONS DISTRIBUTIONS
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Continuous probability distributions Continuous probability distributions Review of discrete and continuous random variables Continuous probability distributions (models) Continuous uniform probability distribution Normal probability distribution Normal approximation to Binomial Correction for continuity Finite Population Correction Factor (FPCF) Exponential distribution
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Review of Discrete and Review of Discrete and Continuous Random Variables Continuous Random Variables A discrete random variable discrete random variable is a variable that can take on a countable number of possible values. continuous random variable continuous random variable  is a  variable that can take on any of the  possible values between two points.
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Examples of Continuous Random Examples of Continuous Random variables variables Time required to perform a job Financial ratios Product weights Volume of soft drink in a 12-ounce can Interest rates Income levels Distance between two points
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Continuous Probability Continuous Probability Distributions Distributions The probability distribution can be represented as a function: f(x) f(x) is called a probability density function Because X can take an infinite amount of values, you can not define the probability at any exact point So we cannot calculate P(X=x) Note we can calculate the probability that x is within a very very small interval using derivatives: f(x)dx
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Continuous Probability Continuous Probability Distributions Distributions We have to calculate the probability over an interval: P(X<a), or P(X>b) or P(a<X<b) this is done using integrals • The probability is the area under the curve between a and b • The total area under the curve MUST equal 1 The special case of P(X<x) (the probability that X is less than or equal to some value) is called the cumulative probability • The collection of the cumulative probability of ALL possible values of X is a function defined as the integral of f(x), F(x) = P(X<x) F(x) is the cumulative probability distribution
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Continuous Probability Continuous Probability Distributions Distributions The probability distribution of a continuous random variable is represented by a probability density function probability density function that defines a curve.
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Continuous Probability Continuous Probability Distributions Distributions x f(X) P(X) Possible Values of x x Possible Values of x (a) Discrete Probability  Distribution (b) Probability Density  Function Discrete Continuous
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Reading Probabilities from  Distributions Distributions x f(X) P(X) x 1 2 3 1 2 3 What is the probability that x = 2? 2 < x < 3?
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This note was uploaded on 02/13/2011 for the course ADM na taught by Professor Na during the Winter '09 term at University of Ottawa.

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Continuous Distributions F10 - CONTINUOUS PROBABILITY...

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