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lect9v2_1up - Stat 104: Quantitative Methods for Economists...

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Stat 104: Quantitative Methods for Economists Class 9: Introduction to Probability, Part II 1
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What were we talking about ? s What is probability s Random experiment, events s Joint Probability, Marginal Probability 2
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Conditional Probability s Conditional probabilities ask, what is the chance that A happens, given that we know B happened ? s If the package doesn’t make it to Chicago by 9am tomorrow, what’s the chance we lose the deal ?” s “given we spend 10 million on research, what is the probability of inventing a successful competitor to the Ipod ? s Note the use of the words “if” and “given” 3
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We're selling Talking Elmo Dolls, and we want to know how effective our ad is. Of the people who saw our ad, what percent bought the product? Of those who didn't see the ad? Talking Elmo Example Saw Ad Didn't See Ad Bought 0.2 0.1 0.3 Didn't Buy 0.3 0.4 0.7 0.5 0.5 1 Y X Is this a legal probability table (why) ? 4
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Marginal probabilities are also called unconditional probabilities . From the table, what is the probability that someone bought an Elmo doll ? _______ The question of interest to Fisher-Price : is advertising effective ? That is, what if we first discover that someone saw an ad for Talking Elmo. What is the chance now that the person bought a doll ? 5
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We are looking for P(Bought Elmo|saw ad) which is read as the probability the consumer buys an Elmo given the consumer saw an ad for Elmo. eally we want this probability to be above 30%, Ideally we want this probability to be above 30%, indicating that the advertising is effective. This type of probability is called a conditional probability and is always denoted with the vertical bar “|”. 6
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( ) ( ) = ( | ) P A and B P A B P B Out of all the times B happens, how often does A also happen ? Definition of conditional probability P(Bought elmo|saw ad) = _________ P(Bought elmo|didn’t see ad) = ________ These results indicate that advertising is not working working 7
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Example s Given you like Sprite, what is the probability that you’re a male ? Sierra Mist Sprite ale .4 .15 8 Male 0.4 0.15 Female 0.22 0.23
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One of the objectives of calculating conditional probability is to determine whether two events are related. In particular, we would like to know whether they are independent , that is, if the probability of one event is not affected by the occurrence of the other event. Independence Two events A and B are said to be independent if P(A|B) = P(A) or P(B|A) = P(B) If A and B are not independent, they are called dependent. 9
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P(bought | Seen ad) = 40% and P(bought) = 30% we can see that having seen the ad effects the probability of buying a Talking Elmo. Recall Talking Elmo Example In fact we can conclude that seeing the ad is effective in increasing sales and would say that the probability of buying a Potty Elmo depends on whether or not the customer saw an ad. 10
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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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lect9v2_1up - Stat 104: Quantitative Methods for Economists...

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