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CommonRVs - Learning Objectives Recognize and use the...

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Learning Objectives Recognize and use the probability mass functions of common discrete random variables: Uniform Bernoulli Binomial Geometric Poisson
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Discrete Uniform p X ( k ) = 1 b - a + 1 if k = a , a + 1 , K , b 0 otherw ise a b 1/(b-a+1)
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Example p X ( k ) = 1 5 - 3 + 1 = 0.33 if k = 3 ,4,5 0 otherw ise a = 3 b = 5
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Exercises Exercise #141 Exercise #142
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p X ( x ) = p , if x =1 1- p , if x = 0 Bernoulli model situations with two outcomes PMF:
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Example Tossing a fair coin P(heads) = 0.5 P(tails) = 0.5 if Heads then X = 1 if Tails then X = 0 p X ( x ) = 0.5, if x =1 1-0.5, if x = 0
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Example A person is either sick or healthy P(disease) = 0.3 P(normal) = 0.7 if Disease then X = 1 if Normal then X = 0 p X ( x ) = 0.3 , if x =1 1-0.3, if x = 0
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Exercise Exercise #7
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Binomial Constructed from a sequence of n Bernoulli RV’s with parameter p Binomial RV is the number of “successes” k in n trials Binomial RV X with parameters n and p PMF: p X ( k ) = n k p k (1 - p ) n - k k = 0 ,1 , K , n
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