lect14v3_1up

lect14v3_1up - Stat 104: Quantitative Methods for...

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Stat 104: Quantitative Methods for Economists Class 14: Continuous Probability Distributions 1
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The major distinction between a continuous and discrete random variable is the numerical events of interest. Discrete versus Continuous 2 We can list all possible values of a discrete random variable, and it is meaningful to consider the probability that a particular individual value will be assumed.
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We cannot list all the values of a continuous random variable-because there is always another possible value between any two of its values. Hence the only meaningful events for a ontinuous random variable are tervals. 3 continuous random variable are intervals. The probability that a continuous random variable X will assume any particular value is 0 .
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P(X=x) = 0 for any x if X is a continuous random variable Huh ?? Let’s try to give a basic argument For a six sided die, what is the probability of rolling a 3 ? For a 20 sided die, what is the probability of rolling a 3 ? 4 Several polyhedra in various materials with similar symbols are known from the Roman period. Modern scholarship has not yet established the game for which these dice were used. For a 100 sided die, what is the probability of rolling a 3 ?
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Two things (related) •What is happening to the probability of rolling a 3 ? •What is happening to the shape of the die ? The basic axiom of probability says that the sum of all the outcome probabilities must be 1. 5 If we continue with the die example, it will be impossible to assign positive probability to each outcome so that they all sum to 1. P(X=x) = 0 for any x if X is a continuous random variable
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P(X=x) = 0 for any x if X is a continuous random variable Hence, for a continuous random variable X, it is only meaningful to talk about the probability that the value assumed by X will fall within some interval of values . 6 ( ) P a X b
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Examples of continuous random variables: Length of time between arrivals at a hospital clinic, weight of a food item bought at a supermarket, amount of soda in a 12 oz can, eight of sunspots, 7 height of sunspots, a person’s hat size.
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Density Curves s Graphs are usually the easiest way to describe a continuous random variable. s
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lect14v3_1up - Stat 104: Quantitative Methods for...

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