discretenotes

# discretenotes - De.nitions and other formulas Sections 3.1...

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De…nitions and other formulas - Sections 3.1 to 3.3 De…nition 1 A random variable is any rule which associates a number with each outcome in a sample space. De…nition 2 Any random variable whose only possible values are 0 and 1 is called a Bernoulli random variable . De…nition 3 A set is discrete either if it consists of a …nite number of elements or if its elements can be listed in sequence so that there is a …rst element, a second element, a third element, and so on, in the list. De…nition 4 A random variable is said to be discrete if its set of possible values is a discrete set. De…nition 5 The probability distribution or probability mass function (pmf) of a discrete random variable is de…ned for every number x by p ( x ) = P ( X = x ) = P ( all s 2 S : X ( s ) = x ) . De…nition 6 Suppose p ( x ) depends on a quantity that can be assigned any one of a number of possible values, with each di¤erent value determining a di¤erent probability distribution. Such a quantity is called a

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discretenotes - De.nitions and other formulas Sections 3.1...

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