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POLS 3650 January 27 2014 Lectures VI- VII.docx

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Department
Political Science
Course Code
POLS 3650
Professor
Edward Koning

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POLS 3650 January 27 2014 Lectures VI (continued)­ VII Probability of One Event or Another ­ When you want to calculate the probability of one outcome or another, apply the  addition rule of probabilities ­ p(A or B)= p(A) + p(B) ­ Example what is the probability that we roll a 2 or a 4? ­ P (2­4)= p(2) +p(4) Mutually Exclusive events or not? ­ Mutually Exclusive events cannot both occur at the same time ­ Non­ Mutually exclusive events can occur at the same time o In these cases, we need to avoid ‘double counting’: o p(A or B)= p(A) + p(B)­ p(A and B) Discrete and Continuous Probabilities  ­ All the examples in this lecture have been of discrete probabilities: probability  calculations based on discrete variables  ­ The probability calculations for continuous variables (age) are slightly different o The chance that a randomly selected individual has an age of exactly  25.00000 is very, very small o We therefore calculate probabilities of for ranges for example 25­26 Key points ­ Probability theory is the basis (GO BACK) ­ THE NORMAL DISTRIBUTION­ Lecture VII Definition and relevance [1/2] o A normal distribution is a distribution with the shape of a bell or clock o (Frequency distribution): how high it is depends on how many cases there  are o It is symmetrical  o Mode= median= mean o The further we move from the mean, the lower the frequency  The height of everyone in the room in a frequency distribution:  average height but some very tall and some very short but most  will have average height  Definition and Relevance [2/2] ­ We know exactly what normal distribution looks like once we know u  (mean)  and o (standard deviation)  ­ We use this information in statistical inference  ­ Look at slide Deviations from normality [1/3] ­ Three characteristics are crucial in describing the normality of a distribution o 50/50 normal distribution are symmetrical others are skewed  One mode  1 o Skewed to the right (positively skewed) o Skewed to the left (negatively skewed) Deviations from normality [2/3] o Normal distributions are unimodal, others are not  Bimodal • Two modes  Multimodal  Deviations from normality [3/3] ­ Normal distributions are mesokurtic  o (They hav
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