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2303RandomVariables F10

2303RandomVariables F10 - RANDOM VARIABLES RANDOM Random...

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RANDOM VARIABLES RANDOM VARIABLES
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Random Variables Random Variables Introduction to random variables Discrete random variables Introduction to probability models Expected value and variance Operations on random variables
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Random Variables Random Variables A random variable assumes a value based on the outcome of a random event. We use a capital letter, like X , to denote a random variable. A particular value of a random variable will be denoted with a lower case letter, in this case x .
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Types of Random Variables Types of Random Variables Discrete random variables can take one of a finite number of distinct outcomes. Examples: Number of credit hours Number of defective units, … Continuous random variables can take any numeric value within a range of values. Examples: Cost of books this term Profit, productivity, physical measurements of distance, time, temperature, pressure, pollution,…
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Discrete Random Variables Discrete Random Variables Can only assume a countable number of values Examples: Roll a die twice Let x be the number of times 4 comes up (then x could be 0, 1, or 2 times) Toss a coin 5 times. Let x be the number of heads (then x = 0, 1, 2, 3, 4, or 5)
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Experiment: Toss 2 Coins. Let x = # heads. T T Discrete Probability Distribution Discrete Probability Distribution 4 possible outcomes T T H H H H Probability Distribution 0 1 2 x x Value Probability 0 1/4 = .25 1 2/4 = .50 2 1/4 = .25 . 50 .25 Probability
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A probability model for a random variable consists of: The collection of all possible values of a random variable, and The probabilities that the values occur. Probability Model Probability Model
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Discrete Probability Distribution Discrete Probability Distribution
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Expected Value (mean) of a Expected Value (mean) of a discrete distribution discrete distribution The expected value of a random variable can be found by summing the products of each possible value by the probability that it occurs: Expected Value of a discrete distribution (Weighted Average) E(x) = Σ x i P(x i )
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