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PSYC 210 - Binomial Distributions

PSYC 210 - Binomial Distributions - Binomial Distributions...

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0 1 2 # of heads PROB Binomial Distributions 1. Terms A binomial distribution is the distribution of a binomial variable. Binomial variable: {two names} when a variable is measured on a scale with exactly two categories. Examples: gender, flipping a coin, left hand/right hand, Probability of A = p(A) = number of outcomes classified as A/total number of possible outcomes These categories are mutually exclusive: being in one precludes being in another. 2. Context We generally know the probabilities associated with each of the two categories. For example: coin toss: p(heads) = .5, p(tails) = .5 But we want to know: What is the number of times each category occurs in a series of trials (or in a sample of individuals)? i.e., What is the probability of obtaining 15 heads in 20 coin tosses? What is the probability of obtaining 20 right-handers in a class of 30 students? 3. Notation 1. A & B 2 categories for the variable (A and B) 2. p ’s & q ’s Probability (or proportion) is identified as: p: p(A) = probability of A q: q(B) = probability of B (p&q are the only possible outcomes) and p + q = 1 3. n n
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