University of Oklahoma
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|[pic] |[|Calculus and Analysis [pic]Special Functions [pic]Multivariate Functions [pic] |[|
|[pic] |p|Probability and Statistics [pic]Multivariate Statistics [pic] |p|
| |i|Probability and Statistics [pic]Statistical Distributions [pic]Continuous Distributions [pic] |i|
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|[pic] | |Bivariate Normal Distribution | |
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| | |[pic][pic] | |
|[pic] | |[pic] | |
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|[pic] | |The bivariate normal distribution is given by | |
|[pic] | |[pic] | |
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|INDEX | | | |
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|Algebra | |where | |
|[pic] | |[pic] | |
| | |(2) | |
|Applied Mathematics | | | |
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|Calculus and | |and | |
|Analysis | |[pic] | |
|[pic] | |(3) | |
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|Discrete Mathematics| | | |
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| | |is the correlation of [pic]and [pic](Kenney and Keeping 1951, pp. 92 and 202-205; Whittaker and Robinson | |
|Foundations of | |1967, p. 329). Note that | |
|Mathematics | |[pic] | |
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|Geometry | |(4) | |
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|History and | |[pic] | |
|Terminology | |[pic] | |
|[pic] | |(5) | |
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|Number Theory | |[pic] | |
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|Probability and | |(6) | |
|Statistics | | | |
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| | |are commonly used in place of [pic]and [pic]. | |
|Recreational | |The probability function of the bivariate normal distribution is implemented as | |
|Mathematics | |PDF[MultinormalDistribution[{mu1, mu2}, {{sigma11, sigma12}, {sigma12, sigma22}}], {x1, x2}] in the | |
|[pic] | |Mathematica add-on package Statistics`MultinormalDistribution` (which can be loaded with the command | |
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