L17_RandomVariables

L17_RandomVariables - COMP170 Discrete Mathematical Tools...

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1-1 COMP170 Discrete Mathematical Tools for Computer Science Discrete Math for Computer Science K. Bogart, C. Stein and R.L. Drysdale Section 5.4, pp. 249-262 Random Variables Version 2.0: Last updated, May 13, 2007 Slides c 2005 by M. J. Golin and G. Trippen
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2-1 Random Variables What Are Random Variables? Binomial Probabilities Expected Values Expected Values of Sums and Numerical Multiples Indicator Random Variables The Number of Trials until a First Success
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3-1 What Are Random Variables?
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3-2 What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S .
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3-3 Flipping a coin n times. What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S . Example
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3-4 Flipping a coin n times. Sample space: set of all sequences of n H ’s and T ’s. What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S . Example
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3-5 Flipping a coin n times. Sample space: set of all sequences of n H ’s and T ’s. What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S . Example Random variable “number of heads” takes a sequence and tells us how many heads are in that sequence.
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3-6 Flipping a coin n times. Sample space: set of all sequences of n H ’s and T ’s. What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S . Example Random variable “number of heads” takes a sequence and tells us how many heads are in that sequence. Example:
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3-7 Flipping a coin n times. Sample space: set of all sequences of n H ’s and T ’s. What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S . Example Random variable “number of heads” takes a sequence and tells us how many heads are in that sequence. Example: X ( HTHHT ) = 3 .
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3-8 Flipping a coin n times. Sample space: set of all sequences of n H ’s and T ’s. What Are Random Variables? A random variable for an experiment with sample space S is a function that assigns a number to each element of S . Example Random variable “number of heads” takes a sequence and tells us how many heads are in that sequence. Example: X ( HTHHT ) = 3 . X ( THTHT ) = 2 .
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4-1 Example 2: Rolling two dice Random variable is “sum of the values showing on top of dice” .
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4-2 Example 2: Rolling two dice Random variable is “sum of the values showing on top of dice” . X ( ) = 5
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4-3 Example 2: Rolling two dice Random variable is “sum of the values showing on top of dice” .
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