1. CS723 - Probability and Stochastic Processes

2. Lecture No. 17

3. In Previous Lectures
Analysis of continuous random variables Uniform, exponential, Erlang, and Gaussian RV
Gaussian random variable with PDF given by Sqrt(λ/π)e-λx2 has a variance of 1/2λ
Gaussian PDF numerically integrated only for zero mean and unit variance RV
Zero mean Gaussian RV with variance of 2 has a PDF Sqrt(1/2π2 ) e-(x//sqrt(2))2
Transform any Gaussian RV to equivalent zero mean unit variance Gaussian RV before numerical processing

4. Scaling of Gaussian RV

5. Standard Gaussian Events

6. Joint Distributions
Observation of two continuous-valued quantities simultaneously
PDF fXY(x,y) is a function of two variables (hill) representing relative likelihood of a certain pair of observed values
There are marginal densities that can be obtained from the joint PDF
Events are regions of XY plane and probability of an event is the volume of the hill over the region of the event
The total volume of the hill must be equal to 1

7. Pair of Random Variables

8. Pair of Random Variables

9. Pair of Random Variables

10. Pair of Random Variables