A Joint Distribution of Discrete Random Variables

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A Joint Distribution of Discrete Random Variables
X X X
1 2 3
1 0.15 0.2 0.15 0.5 Marginal
Y 2 0.07 0.14 0.09 0.3 Distribution
3 0.05 0.05 0.1 0.2 Of Y
0.27 0.39 0.34
Marginal Distribution of X Marginal Distribution of X Marginal Distribution of X
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Bivariate U((0,1),(0,1))
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Bivariate Normal Distribution
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Three Senators Article I impeachment
votesEight possible outcomes
Lott Wellstone Lieberman
1 1 1
1 1 0
1 0 1
1 0 0
0 0 0
0 1 1
0 1 0
0 0 1
Prob IF p1/4
p3 1/64
p2(1-p) 3/64
p2(1-p) 3/64
p(1-p)2 9/64
(1-p)3 27/64
p2(1-p) 3/64
p(1-p)2 9/64
p(1-p)2 9/64
Observed
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Bernoulli Likelihood Function, Three observation
case
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The Effect of k(y)
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Two Extrema
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The MLE
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Bernoulli Likelihood and Log-likelihood, three
observation case
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Ln(exports) by country, 2001