1. What is a Bivariate Normal Distribution?
IMPORTANT!
1. The “regular” normal distribution has one random variable.
2. A bivariate normal distribution is made up of two independent random variables.
The two variables in a bivariate normal are both are normally distributed, and they have a
normal distribution when both are added together.
Visually, the bivariate normal distribution is a three-
dimensional bell curve.
2. PDF of the Bivariate Normal Distribution.
For any x value between the maximum &
minimum point on the x-axis
For any y value between the maximum &
minimum point on the y-axis
The probability of the 1ste & 2nd variables
standard deviation must be greater than 0.
The correlation coefficient is between -1 & 1.if
the value is between -1 & 1 than the variables
are dependent.
, Examples:
We can see that this pdf displays a general bell-shaped appearance. It looks like a mountain
of normal distribution curves. The surface is centered at the point (μ1, μ2), that is,
the centroid. This distribution is also referred to as two-dimensional Normal.
Parameters:
IMPORTANT!
1. The “regular” normal distribution has one random variable.
2. A bivariate normal distribution is made up of two independent random variables.
The two variables in a bivariate normal are both are normally distributed, and they have a
normal distribution when both are added together.
Visually, the bivariate normal distribution is a three-
dimensional bell curve.
2. PDF of the Bivariate Normal Distribution.
For any x value between the maximum &
minimum point on the x-axis
For any y value between the maximum &
minimum point on the y-axis
The probability of the 1ste & 2nd variables
standard deviation must be greater than 0.
The correlation coefficient is between -1 & 1.if
the value is between -1 & 1 than the variables
are dependent.
, Examples:
We can see that this pdf displays a general bell-shaped appearance. It looks like a mountain
of normal distribution curves. The surface is centered at the point (μ1, μ2), that is,
the centroid. This distribution is also referred to as two-dimensional Normal.
Parameters:
