Math a Discrete Random Variables

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Presentation transcript:

Math 4030-3a Discrete Random Variables

Random variable A function that assigns a numerical value to each possible outcome in the sample space. 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. Sample space S R 5/28/2018

Probability Distribution of a discrete random variable: 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. 5/28/2018

Probability histogram and bar chart; Cumulative distribution function F(x): If X takes values then 5/28/2018

Mean of a random variable Mean may or may not exist; Even exists, may or may not be a finite number; If X has only finitely many values, then mean exists and is a finite value. Average value Balance point Expect value 5/28/2018

Properties of Means: Linearity: Warning: 5/28/2018

Variance of a random variable Variance is a “mean”; Always nonnegative; Variance may or may not exist; Even exists, may or may not be a finite number; If X has only finitely many values, then variance exists and is a finite value. Measure the variability of X Spread of the histogram Un-predictable, risky, … 5/28/2018

Properties of variance Warning: 5/28/2018

Chebyshev’s Theorem If X is a random variable with mean  and standard deviation , then for any number k > 1, Equivalently, 5/28/2018