Statistics A twodimensional random variable with a uniform

Statistics

A two-dimensional random variable with a uniform distribution

A two-dimensional random variable with a uniform distribution

A two-dimensional random variable with a uniform distribution

A two-dimensional random variable with a uniform distribution

A two-dimensional random variable with a uniform distribution variable 2 variable 1

Probability density function for variable 1 probability value

A two-dimensional random variable with a uniform distribution variable 2 variable 1

Probability density function for variable 2 probability value

A two-dimensional random variable with a multi-normal distribution variable 2 variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 Marginal probability density function - variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 Marginal probability density function - variable 1 mean variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 Marginal probability density function - variable 1 standard deviation mean variable 1

A single random variable with a multi-normal distribution standard deviation mean

A two-dimensional random variable with a multi-normal distribution variable 2 standard deviation mean marginal probability density function - variable 2 variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 conditional probability density function - variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 conditional probability density function - variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 conditional probability density function - variable 1

Two-dimensional probability density function

To characterise a single random variable we need…. .

A single random variable with a multi-normal distribution standard deviation mean

mean value variance µ σ2

To characterise two random variables we need…. .

A two-dimensional random variable with a multi-normal distribution variable 2 variable 1

mean values µ 1 µ 2 variance-covariance matrix σ12 σ21 σ22

mean values µ 1 µ 2 variance-covariance matrix σ12 σ21 σ22

A two-dimensional random variable with a multi-normal distribution variable 2 Marginal probability density function - variable 1 standard deviation mean variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 standard deviation mean marginal probability density function - variable 2 variable 1

mean values µ 1 µ 2 variance-covariance matrix σ12 σ21 σ22

A two-dimensional random variable with a multi-normal distribution variable 2 Parameter correlation variable 1

A two-dimensional random variable with a multi-normal distribution variable 2 No parameter correlation variable 1

mean values µ 1 µ 2 variance-covariance matrix σ12 0 0 σ22