Week4[1] - Week 4: Probability Distributions Discrete Data...

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Click to edit Master subtitle style Week 4: Probability Distributions Discrete Data Distributions
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Random Variables and Probability Distributions l Statistical Experiment -- a process by which an observation or measurement is obtained l The quantitative variable x is random when its outcome in an experiment is a factor of chance, its outcome is unpredictable
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A random variable, x is the numerical outcome of a probability experiment A random variable is discrete if the number of possible outcomes is finite or countable. Discrete random variables are determined by a count. A random variable is continuous if it can take on any value within an interval. The possible outcomes cannot be listed. Continuous random variables are determined by a measure. Random Variables Two types of random variables x = The number of people in a car. x = The gallons of gas bought in a week. x = The time it takes to drive from home to school x = The number of trips to school you make per week
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Types of Random Variables x = The number of people in a car. x = The gallons of gas bought in a week. x = The time it takes to drive from home to school x = The number of trips to school you make per week Which of the following are discrete and which are continuous random variables? Discrete - you count the number of people in a car 0, 1, 2, 3… Possible values can be listed. Continuous - you measure the gallons of gas. You cannot list the possible values. Continuous - you measure the amount of time. The possible values cannot be listed. Discrete - you count the number of trips you make. The possible numbers can be listed.
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Whole number (0, 1, 2, 3 etc.) Obtained by counting Usually finite number of values l Poisson random variable is exception # of TV's per Home # of Households % 0 25 2.5% 1 123 12.3% 2 343 34.3% 3 227 22.7% 4 136 13.6% 5 75 7.5% 6 54 5.4% 7 17 1.7% 1000 100.0% Discrete Random Variable
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l List of all possible [ x , P (x) ] pairs x = Value of random variable (outcome) P (x) = Probability associated with value l Mutually exclusive (no overlap) l Collectively exhaustive (nothing left out) l 0 < P (x) < 1 l l P (x) = 1 # of TV's per Home # of Households % 0 25 2.5% 1 123 12.3% 2 343 34.3% 3 227 22.7% 4 136 13.6% 5 75 7.5% 6 54 5.4% 7 17 1.7% 1000 100.0% Discrete Probability Distribution
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Discrete Probability Distributions A discrete probability distribution
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Week4[1] - Week 4: Probability Distributions Discrete Data...

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