L17_RandomVariables

L17_RandomVariables - 1-1COMP170Discrete Mathematical...

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Unformatted text preview: 1-1COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 5.4, pp. 249-262Random VariablesVersion 2.0: Last updated, May 13, 2007Slidesc2005 by M. J. Golin and G. Trippen2-1Random 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 Success3-1What Are Random Variables?3-2What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.3-3Flipping a coinntimes.What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.Example3-4Flipping a coinntimes.Sample space: set of all sequences ofnH’s andT’s.What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.Example3-5Flipping a coinntimes.Sample space: set of all sequences ofnH’s andT’s.What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.ExampleRandom variable“number of heads”takes a sequence and tellsus how many heads are in that sequence.3-6Flipping a coinntimes.Sample space: set of all sequences ofnH’s andT’s.What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.ExampleRandom variable“number of heads”takes a sequence and tellsus how many heads are in that sequence.Example:3-7Flipping a coinntimes.Sample space: set of all sequences ofnH’s andT’s.What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.ExampleRandom variable“number of heads”takes a sequence and tellsus how many heads are in that sequence.Example:X(HTHHT) = 3.3-8Flipping a coinntimes.Sample space: set of all sequences ofnH’s andT’s.What Are Random Variables?Arandom variablefor an experiment withsample spaceSis afunctionthatassigns a numberto each element ofS.ExampleRandom variable“number of heads”takes a sequence and tellsus how many heads are in that sequence.Example:X(HTHHT) = 3.X(THTHT) = 2.4-1Example 2:Rolling two diceRandom variable is“sum of the values showing on top of dice”.4-2Example 2:Rolling two diceRandom variable is“sum of the values showing on top of dice”.X()= 54-3Example 2:Rolling two diceRandom variable is“sum of the values showing on top of dice”.X()= 5X()= 105-1Random 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 Success6-1Bernoulli Random Variables6-2Bernoulli Random VariablesA test in which the outcome is either asuccessorfailure.6-3Bernoulli Random VariablesA test in which the outcome is either a...
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This note was uploaded on 08/25/2010 for the course COMP COMP170 taught by Professor M.j.golin during the Spring '10 term at HKUST.

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L17_RandomVariables - 1-1COMP170Discrete Mathematical...

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