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Math 4030-3b (Discrete) Random Variables, Binomial Distribution
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Random variable (Sec. 4.1) A function that assigns a numerical value to each possible outcome in the sample space. 11/11/20152 Sample space S One value for one outcome. i.e. different value must mean different outcomes. However, different outcomes may have the same value. Random variable may take discrete or continuous values.
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Probability Distribution of a discrete random variable: 11/11/2015 A list of probability values corresponding to all values of a discrete random variable X. i.e. for any value x that the random variable X takes.
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11/11/20154 Probability histogram and bar chart; Cumulative distribution function F(x): If X takes values then
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11/11/20155 Binomial distribution (Sec. 4.2) 1. The experiment consists n trials, each have two outcomes: S or F (Bernoulli Trials) 2. Probability of success are the same in each Bernoulli trial, say p. 3. The n trials are independent. Let X = number of successes in n trials.
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11/11/20156 The probability distribution of X: Cumulative distribution: Table 1 on Page 505.
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11/11/20157 Means and Variances (Sec. 4.4) If X is a discrete random variable that takes the values of with probabilities Mean or (mathematical) expectation is defined as Variance and the standard deviation are or
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11/11/20158 Mean and Variance: Sampling with or without replacement: With replacement: Without replacement:
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