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NotesSep3

# NotesSep3 - Two main types of random variables Discrete...

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Two main types of random variables Discrete random variables A r.v. X is discrete if the set of its possible values is discrete: { a i } , i.e. is ﬁnite or inﬁnite countable. Probability mass function ( pmf ) of a discrete random variable X : p X ( a i ) = P ( X = a i ) , a i a possible value of X. The notation p ( a i ) instead of p X ( a i ) will some- times be used if it is clear what random variable we have in mind.

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For a discrete random variable X and any set B P ( X B ) = X a i B p X ( a i ) . In particular, F X ( x ) = X a i x p X ( a i ) , -∞ < x < .
Continuous random variables A r.v. X is con- tinuous if it has a density . Probability density function ( pdf ), or, simply, density of a continuous random variable X is a nonnegative function f X ( x ) such that for any set B P ( X B ) = Z B f X ( y ) dy. In particular, F X ( x ) = Z x -∞ f X ( y ) dy.

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Note : There are random variables that are neither discrete nor continuous
Terminology : Specifying the distribution of a

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NotesSep3 - Two main types of random variables Discrete...

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