4_Probability_handouts

# 4_Probability_handouts - STAT 5615 Statistics in Research...

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STAT 5615 Statistics in Research (I) Probability Ott & Longnecker 4.1-4.4

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Probability Example: A population of size N = 8 might consists of {1,0,0,2,1,1,1,2}, or equivalently, 3 distinct values 0, 1, 2 with respective frequencies 2, 4, 2. What are the chances that the outcome of a single draw is 0? Chances are 2 in 8, or 2/8 = 0.25; this is the relative frequency of 2 in the population Probability of “outcome of a single draw = 0” is 0.25, or P(outcome of single draw = 0) = 0.25
Role of Probability The role of probability is to measure uncertainty and to quantify the confidence in our conclusions. Example: I have five dice and need to determine if they are loaded such that larger values are more likely. Roll the dice. Suppose we get five 6’s. What do you think? Assume dice are fair: P(five 6’s)=? 0.00013 If the dice are fair, then there is a very small chance we would see such convincing evidence simply by chance. The number above is called a p -value (more on this later).

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Probability Sample Population Statistics Probability Example : A jar of M&M’s contains 100 candies, 15 of which are red. We take out 10 of these. What is the chance that 3 of the 10 are red? Inferential Statistics Example : A handful of 10 M&M’s is selected from a jar containing 1000 candy pieces. Three in the handful are red. What is the proportion of red M&M’s in the entire jar?
Assigning Probabilities to Events Random experiment a process of observation or measurement that has an uncertain outcome.

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Sample Space Ω list of all possible outcomes of the experiment. The outcomes must be mutually exclusive and exhaustive. Discrete: outcome of rolling a die Ω = {1, 2, 3,
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## This note was uploaded on 09/11/2008 for the course STAT 5615 taught by Professor Pdu during the Fall '08 term at Virginia Tech.

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4_Probability_handouts - STAT 5615 Statistics in Research...

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