Math 4030-3b (Discrete) Random Variables, Binomial Distribution.

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Presentation transcript:

Math b (Discrete) Random Variables, Binomial Distribution

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.

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.

11/11/20154 Probability histogram and bar chart; Cumulative distribution function F(x): If X takes values then

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.

11/11/20156 The probability distribution of X: Cumulative distribution: Table 1 on Page 505.

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

11/11/20158 Mean and Variance: Sampling with or without replacement: With replacement: Without replacement: