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Unformatted text preview: Learning Objectives • Calculate the joint probability mass function of two or more discrete random variables. • Define and compare marginal and a conditional mass functions • Calculate the marginal probability mass functions from a joint probability mass function. • Calculate a conditional probability mass function for a discrete random variable conditioned on another discrete random variable. Joint PMF • 2 RVs X and Y from an experiment • probabilities of X and Y are joint PMF p X , Y x , y ( 29 = P ( X = x , Y = y ) RV’s X and Y particular values x and y Example • As an engineering student in a demanding undergraduate program, you find yourself getting many headaches. Intrigued, you decide to study the relationship between a new medication, Niripsa, and frequency of headaches. For most of your sophomore year you keep track of how many days of the week you have headaches and how many Niripsa tablets you take each week. You are a little nervous about overdosing on Niripsa, so you are unwilling to take more than 20 tablets per week. The data from your self experimentation are listed in the table shown. Number of Niripsa taken Joint PMF x y 2 4 6 1 2 3 4 5 6 7 8 9 10 0.02 0.04 0.06 0.08 0.1 p ( x , y ) Marginal PMFs • Get marginal PMFs of X and Y from the joint PMF: p X ( x ) = p X , Y x , y ( 29 y ∑ p Y ( y ) = p X , Y x , y ( 29 x ∑ Marginal PMF 1 3 5 7 9 1 5 9 0.005 0.01 0.015 0.02 0.025 p(x,y) X Y Joint PMF ∑ 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 1 2 3 4 5 6 7 8 9 10 X p(x) p X ( x ) = p X , Y x , y ( 29 y ∑ Marginal PMF...
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 Spring '10
 Dunn
 Trigraph, joint pmf

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