statistics. a two-dimensional random variable with a uniform distribution
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Statistics
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A two-dimensional random variable with a uniform distribution
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A two-dimensional random variable with a uniform distribution
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A two-dimensional random variable with a uniform distribution
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A two-dimensional random variable with a uniform distribution
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A two-dimensional random variable with a uniform distribution
variable 1
variable 2
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Probability density function for variable 1
value
probability
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A two-dimensional random variable with a uniform distribution
variable 1
variable 2
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Probability density function for variable 2
value
probability
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
mean
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
mean
standard deviation
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A single random variable with a multi-normal distribution
mean
standard deviation
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
marginal probability density function - variable 2
mean
standard deviation
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
conditional probability density function - variable 1
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
conditional probability density function - variable 1
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
conditional probability density function - variable 1
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Two-dimensional probability density function
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To characterise a single random variablewe need…..
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A single random variable with a multi-normal distribution
mean
standard deviation
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µ
mean value variance
σ2
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To characterise two random variableswe need…..
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
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µ1 µ2
mean valuesvariance-covariancematrix
σ12 σ12
σ21 σ22
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µ1 µ2
mean valuesvariance-covariancematrix
σ12 σ12
σ21 σ22
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
mean
standard deviation
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
marginal probability density function - variable 2
mean
standard deviation
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µ1 µ2
mean valuesvariance-covariancematrix
σ12 σ12
σ21 σ22
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
Parameter correlation
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A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
No parameter correlation
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µ1 µ2
mean valuesvariance-covariancematrix
σ12 0
0 σ22