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Prelim 2 Study guide

# Prelim 2 Study guide - population. n=sampl

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The population distribution of a variable is the distribution of its values for all members of the population. The population distributeion is also the probability distribution of the variable when we choose one individual at random from the population. For binomial distributions n = sample size (number being sampled) X = the random variable that gives the count of interest (number of “successes) When a random variable has two possible outcomes we use the sample proportion as a summary P hat = X/n Binomial Setting requires: 1. There are a fixed number n of observations 2. The n observations are all independent 3. Each observation falls into one of just two categories, which for convenience we call “success” or failure 4. The probability of success, call it p is the same for each observation The number of heads we count is a random variable X The distribution of X is completely determined by the number of observations n and the prob. P The distribution of the count X of successes in the binomial setting is called the binomial distribution with parameters n and p . The possible values of X are the whole numbers from 0 to n . We say that X is B(n,p)

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