week4 - Random Variables Example: We roll a fair die 6...

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week 4 1 Random Variables Example: We roll a fair die 6 times. Suppose we are interested in the number of 5’s in the 6 rolls. Let X = number of 5’s. Then X could be 0, 1, 2, 3, 4, 5, 6. X = 0 corresponds to the 56 elements of our 66 elements of . X = 1 corresponds to the elements etc. X is an example of a random variable. Probability models often stated terms of random variables. E.g. - model for the # of H’s in 10 flips of a coin. - model for the height of a randomly chosen person. - model for size of a queue.
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week 4 2 Discrete Probability Spaces ( , F , P )
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week 4 3 Discrete Random Variable Definition: A random variable X is said to be discrete if it can take only a finite or countably infinite number of distinct values. A discrete random variable X maps the sample space onto a countable set. Define a probability mass function (pmf) or frequency function on X such that Where the sum is taken over all possible values of X . Note that there is a theorem that states that there exists a probability triple and random variable whenever we have a function p such that Definition: The probability distribution of a discrete random variable X is represented by a formula, a table or a graph which provides the list of all possible values that X can take and the pmf for each value
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week 4 4 Examples of Discrete Random Variables Discrete Uniform Distribution We roll a fair die.
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This note was uploaded on 09/22/2010 for the course STATISTICS STA257 taught by Professor Mcdunnough during the Fall '10 term at University of Toronto- Toronto.

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week4 - Random Variables Example: We roll a fair die 6...

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