Statistics. A two-dimensional random variable with a uniform distribution

Statistics

A two-dimensional random variable with a uniform distribution

variable 1

variable 2

Probability density function for variable 1

probability

A two-dimensional random variable with a uniform distribution

variable 1

variable 2

Probability density function for variable 2

probability

A two-dimensional random variable with a multi-normal distribution

variable 1

variable 2

variable 1

variable 2

variable 1

variable 2

variable 1

variable 2

variable 1

variable 2Marginal probability density function - variable 1

variable 1

standard deviation

A single random variable with a multi-normal distribution

standard deviation

variable 1

variable 2

marginal probability density function - variable 2

standard deviation

variable 1

variable 2

variable 1

variable 2

conditional probability density function - variable 1

variable 1

variable 2

variable 1

variable 2

Two-dimensional probability density function

To characterise a single random variablewe need…..

A single random variable with a multi-normal distribution

standard deviation

mean value variance

To characterise two random variableswe need…..

variable 1

variable 2

µ1 µ2

mean valuesvariance-covariancematrix

σ12 σ12

σ21 σ22

µ1 µ2

σ12 σ12

σ21 σ22

variable 1

standard deviation

variable 1

variable 2

marginal probability density function - variable 2

standard deviation

µ1 µ2

σ12 σ12

σ21 σ22

variable 1

variable 2

Parameter correlation

variable 1

variable 2

No parameter correlation

µ1 µ2

σ12 0

0 σ22

Statistics. A two-dimensional random variable with a uniform distribution

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