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Discrete_RVs

# Discrete_RVs - Some common families of discrete random...

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Some common families of discrete random variables Math 30530, Fall 2012 October 7, 2012 Math 30530 (Fall 2012) Discrete Random Variables October 7, 2012 1 / 10

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The Bernoulli random variable Name : Bernoulli ( p ) When to use : When you want to indicate whether an experiment resulted in success or not; Bernoulli random variable takes value 1 if success occurred, and 0 otherwise Parameter : I p : the probability of success (so p = Pr ( A ) if success is that event A occurred) Mass function : p X ( x ) = p if x = 1 q = 1 - p if x = 0 0 otherwise Statistics : I μ = E ( X ) = p I σ 2 = Var ( X ) = p ( 1 - p ) = pq Math 30530 (Fall 2012) Discrete Random Variables October 7, 2012 2 / 10
The Binomial random variable Name : Binomial ( n , p ) When to use : When you want to count how many successes you had, when you repeat the same experiment a fixed number of times, independently of each other Parameters : I n : the number of times the experiment is repeated I p : the probability of success on each individual trial Mass function : p X ( x ) = ( n x ) p x q n - x if x = 0 , 1 , 2 , . . . , n 0 otherwise where ( n x ) = n ! x !( n - x )! counts the number of ways of distributing x successes among n trials, and n ! = n × ( n - 1 ) × . . . × 3 × 2 × 1 Statistics : I μ = E ( X ) = np I σ 2 = Var ( X ) =

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