# Monson H Hayes- Statistical Signal Processing Chapter 3 --- The study of random variables involves the probabilistic perspective(How the random variable will behave at this point of time using the probability distributions) and the statistical perspective(How will the random variable behave on average). Now to study the RV's probabilistically the distributions(pdf,pmf,cdf) are needed and to study them statistically(expected value,variance,standard deviation) are required. Extending the study of random variables to more than 1 RV we again try viewing them from the probabilistic and statistical perspective and try to understand the dependence between them. Probabilistically we define concepts like joint pdf,pmf and cdf and statistically we define the correlation, covariance to understand how dependent 1 RV is on the other. We draw a boundary between uncorrelation and independence and their mathematical statements. Statistical independence is proved using the probability distributions but to prove 2 random variables are uncorrelated statistical averages like correlation and covariance are needed. <span style="color:red"> Doubt: What is the difference between uncorrelated and independence </span> ### 3.2.6 Linear mean square estimation