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Unformatted text preview: Chapter 3 ■ Random Variables and Probability Distributions 2 Sections 31 through 33 3 Definition: Random Variable ■ Random variable: – A variable whose measured value can change ■ Some examples: – Number of students taking IEE 380 from semester to semester (discrete) – Waiting time in a line at a bank (continuous) – Number of defects on circuit board part number A1425 (discrete) – Men’s heights (continuous) 4 Facts ■ Let P(A) be the probability of any event, A, happening – 0 < P(A) < 1.0 – 1P(A) is the probability that event A does not happen ■ The sum of the probabilities of all possible outcomes must = 1.0 5 Probability vs. Statistics ■ Probability is about CHANCE ■ Statistics are about DATA that estimate CHANCE – This is primarily a statistics course. – You will have to learn some things about probability if you are to understand the statistics we will be doing 6 Probability and Statistics ■ What is probability ? What are statistics ? – Probability deals with predicting the likelihood of future events – Statistics involves the analysis of the frequency of past events – Probability is primarily a theoretical branch of mathematics, which studies the consequences of mathematical definitions – Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world – Probability is what happens in a perfect world – Statistics is what happens in a variable world – Probability deals with the entire population of interest – Statistics deals with samples from the population of interest to draw conclusions about that population 7 Examples ■ To find the chance that a 5 will be thrown on the toss of a die, you toss the die 1,000,000 times and count the number of times a 5 appears to be 166,549. Since 166,549/1,000,000 is very close to 1/6, you conclude that the chance of getting a 5 is 1/6. – Probability or Statistics? ■ To find the chance that a 5 will be thrown on the toss of a die, you reason that there are 6 sides to the die, that the die appears to have no holes or extra weight in it or on any side, that each side is equally likely to appear. You conclude that the chance of getting a 5 is therefore, 1/6. – Probability or Statistics? 8 Population vs. Sample ■ Population – All the people living in AZ ■ Sample of that population – All the people living in Tempe, AZ Population: The scores of every Exam #1 in this class Sample of that population: Josh, Britney and Mike’s Exam #1 scores 9 ■ Population – The resistance values of every resistor part #10089, produced by Acme Electronics, since the beginning of the production run....
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 Summer '09
 chattin
 Normal Distribution, Probability theory, Probability mass function

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