a joint distribution of discrete random variables x 123 10.150.20.150.5marginal...
DESCRIPTION
Bivariate Normal DistributionTRANSCRIPT
![Page 1: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/1.jpg)
A Joint Distribution of A Joint Distribution of Discrete Random VariablesDiscrete Random Variables
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
![Page 2: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/2.jpg)
Bivariate U((0,1),(0,1))Bivariate U((0,1),(0,1))
![Page 3: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/3.jpg)
Bivariate Normal Bivariate Normal DistributionDistribution
![Page 4: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/4.jpg)
Three Senators’ Article I Three Senators’ Article I impeachment votes:impeachment votes:
Eight possible outcomesEight possible outcomesLott 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 p=1/4
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
![Page 5: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/5.jpg)
Bernoulli Likelihood Bernoulli Likelihood Function, Three Function, Three observation caseobservation case
![Page 6: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/6.jpg)
The Effect of The Effect of k(y)k(y)
![Page 7: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/7.jpg)
Two ExtremaTwo Extrema
![Page 8: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/8.jpg)
The MLEThe MLE
MLE
![Page 9: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/9.jpg)
Bernoulli Likelihood and Bernoulli Likelihood and Log-likelihood, three Log-likelihood, three
observation caseobservation case
![Page 10: A Joint Distribution of Discrete Random Variables X 123 10.150.20.150.5Marginal Y20.070.140.090.3Distribution 30.05 0.10.2Of Y 0.270.390.34 Marginal Distribution](https://reader036.vdocuments.us/reader036/viewer/2022062504/5a4d1b717f8b9ab0599b56db/html5/thumbnails/10.jpg)
Ln(exports) by country, Ln(exports) by country, 20012001
Frac
tion
Ln(Exports)2.07944 4.76217
0
.2