1: Densities & Distributions (CDF)
L3 C1
Discrete RV's are easy to understand and manipulate. However, some real world situations can be modelled more conveniently by continuous random variables, to be defined. It should be clearly understood that discrete random variables are SUFFICIENT for all practical purposes. If we take a computer, it has a discrete and finite set of possible values it can assign to numbers. However, when the decimal precision gets very large, it begins to look like a continuous range. The use of continuous random variables occurs because it is computationally convenenient -- it is much simpler to work with, and the calculations are easier -- than a suitable discrete approximation which would suffice for all practical purposes.
The density is most convenient to work with. However, from a mathematical point of view, the CDF is more fundamental. Every variables is uniquely defined by its CDF, and every CDF satisfying the properties listed has a unique random variable associated with it. The first slides defines the density, while the remaining slides develop the properties of the CDF.
S1: Continuous RV's
S2: Cumulative Distribuiton Function (CDF)
S3: Limits at plus and minus infinity of the CDF