Upload
marylou-williams
View
216
Download
0
Embed Size (px)
Citation preview
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 1
variable 2
Probability density function for variable 1
value
probability
A two-dimensional random variable with a uniform distribution
variable 1
variable 2
Probability density function for variable 2
value
probability
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
mean
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
mean
standard deviation
A single random variable with a multi-normal distribution
mean
standard deviation
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
marginal probability density function - variable 2
mean
standard deviation
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
conditional probability density function - variable 1
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
conditional probability density function - variable 1
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
conditional probability density function - variable 1
Two-dimensional probability density function
To characterise a single random variablewe need…..
A single random variable with a multi-normal distribution
mean
standard deviation
µ
mean value variance
σ2
To characterise two random variableswe need…..
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
µ1 µ2
mean valuesvariance-covariancematrix
σ12 σ12
σ21 σ22
µ1 µ2
mean valuesvariance-covariancematrix
σ12 σ12
σ21 σ22
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2Marginal probability density function - variable 1
mean
standard deviation
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
marginal probability density function - variable 2
mean
standard deviation
µ1 µ2
mean valuesvariance-covariancematrix
σ12 σ12
σ21 σ22
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
Parameter correlation
A two-dimensional random variable with a multi-normal distribution
variable 1
variable 2
No parameter correlation
µ1 µ2
mean valuesvariance-covariancematrix
σ12 0
0 σ22