lect13v4_1up

lect13v4_1up - Stat 104: Quantitative Methods for...

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Stat 104: Quantitative Methods for Economists Class 13: Important Discrete Probability Distributions 1
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Let X be a random variable. A probability distribution for X tells us two things: 1) What values X can take on What is a probability distribution ? 2) The chance X takes any particular value. Example: X is a random variable with P(X=0)=.2, P(X=17)=.7, P(X=3.1415)=.3 the probability distribution 2
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s A discrete random variable is a variable that can assume only a countable number of values Many possible outcomes: umber of complaints per day Discrete Probability Distributions b number of complaints per day b number of TV’s in a household b number of rings before the phone is answered Only two possible outcomes: b gender: male or female b defective: yes or no b likes window seat/hates window seat 3
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Continuous Probability Distributions s A continuous random variable is a variable that can assume any value on a continuum (can assume an uncountable number of values) ickness of an item b thickness of an item b time required to complete a task b temperature of a solution b height, in inches s These can potentially take on any value, depending only on the ability to measure accurately. 4
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How many probability distributions exist ? A lot (more than a googool). How many will we learn ? About 3. Maybe 4. he ost ommon iscrete robability The most common discrete probability distribution is the Binomial Distribution. The most common continuous distribution is the Normal distribution. These 2 distributions occur in the real world quite a bit and are useful in modeling real world phenomena. 5
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Probability Distributions Continuous Probability Distributions Probability Distributions Discrete Probability Distributions Binomial Poisson Normal Uniform Exponential 6
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The Binomial Distribution s Characteristics of the Binomial Distribution : b The binomial models n instances of a trial which has only two possible outcomes – “success” or “failure” b There is a fixed number, n , of identical trials b The trials of the experiment are independent of each other b The probability of a success, p , remains constant from trial to trial b If p represents the probability of a success, then (1- p ) = q is the probability of a failure b We are interested in the total number of successes (out of n trials) 7
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Independent Trial Examples s A manufacturing plant labels items as either defective or acceptable s
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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lect13v4_1up - Stat 104: Quantitative Methods for...

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