05_Chapter 3

# 05_Chapter 3 - Chapter 3 Discrete Random Variables and...

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Chapter 3 Discrete Random Variables and Probability Distributions 3.1 Random Variables A random variable (r. v.) is any rule that associates a number with each outcome in the sample space S . Random variables are denoted by capital letters (i.e., X , Y , Z ), and values of random variables are denoted by corresponding lower case letters. Example : Toss a coin three times. Let X = number of heads in three tosses. Example : Sample a product from an assembly line. Let X = life-length of the item. Bernoulli experiment – in an experiment with a binary outcome, such as success/failure, we will define the random variable success -> 1; failure -> 0. 17

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Recall from Chapter 1: Discrete Random Variable - Countable, “jumps” from one possible value to the next, “The number of …,” assumes distinct values (usually a count), finite or infinitely countable Examples : A Bernoulli experiment provides a 0/1 response. A binomial r. v. gives the number of successes in n independent, identical trials. Possible values are 0, 1, . .., n . A geometric r.v. gives the number of objects tested until a success. Possible values are 1, 2, 3, . ... Continuous Random Variable - Possible values consist of an entire interval on the number line: time, depth, weight, etc.; can assume any value in a finite or infinite interval Examples : Measurements: Select a random location in the continental U.S. and measure the height above sea level. The result could be any value in the approximate range [-290, 14500]. Time to failure: The result is potentially any positive number. 18
3.2 Probability Distributions for Discrete Random Variables A discrete distribution is described by giving its probability mass function (pmf), denoted p ( x ), either as a table or as a function. Properties:

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## 05_Chapter 3 - Chapter 3 Discrete Random Variables and...

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