
2DRandom Variables
Let X and Y be two random variables defined on the same sample space S. Then the function (X,Y) that assigns a point in is called a two dimensional random variable. Examples: Joint CDF of (X,Y): The joint cdf of (X,Y) is defined as: Properties of CDF: Proof of Property 1: PROOF OF PROPERTY 2:…

Normal Distribution
A random variable X is said to follow a Normal Distribution with parameters and if it has a probability density function given by: A random variable X is said to follow a Normal Distribution with parameters and if it has a distribution function given by: First Four Moments: Skewness and Kurtosis Some Interesting Properties of…