Discrete Random Variables

That x takes on is nite or countable x is discrete

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Unformatted text preview: a random variable If set of values that X takes on is finite or countable, X is discrete For each x ∈ R, {ω |X (ω ) = x } = {X = x } = “X = x is an event (Probability) mass function of X : for each x ∈ R pX (x ) = Pr(X = x ) Math 30530 (Fall 2012) Discrete RVs September 18, 2013 2/2 Setup for discrete random variables To each outcome ω of experiment, assign numerical value X (ω ) Function X : Ω → R is a random variable If set of values that X takes on is finite or countable, X is discrete For each x ∈ R, {ω |X (ω ) = x } = {X = x } = “X = x is an event (Probability) mass function of X : for each x ∈ R pX (x ) = Pr(X = x ) Basic facts about mass function: pX (x ) ≥ 0 always Math 30530 (Fall 2012) Discrete RVs September 18, 2013 2/2 Setup for discrete random variables To each outcome ω of experiment, assign numerical value X (ω ) Function X : Ω → R is a random variable If set of values that X takes on is finite or countable, X is discrete For each x ∈ R, {ω |X (ω ) = x } = {X = x } = “X = x is an event (Probability) mass function of X : for each x ∈ R pX (x ) = Pr(X = x ) Basic facts about mass function: pX (x ) ≥ 0 always x ∈R pX (x ) = 1 Math 30530 (Fall 2012) Discrete RVs September 18, 2013 2/2 Setup for discrete random variables To each outcome ω of experiment, assign numerical value X (ω ) Function X : Ω → R is a random variable If set of values that X takes on is finite or countable, X is discrete For each x ∈ R, {ω |X (ω ) = x } = {X = x } = “X = x is an event (Probability) mass function of X : for each x ∈ R pX (x ) = Pr(X = x ) Basic facts about mass function: pX (x ) ≥ 0 always x ∈R pX (x ) = 1 Think of random variable as a tool to focus on what’s important about the outcome of an experiment Math 30530 (Fall 2012) Discrete RVs September 18, 2013 2/2...
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This note was uploaded on 01/31/2014 for the course MATH 30530 taught by Professor Hind,r during the Fall '08 term at Notre Dame.

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