Other Selected Topics in Basic Probability

Abstract

In the first part of this chapter, the basic terms related to the jointly distributed random variables including the joint probability mass function and joint probability density function, sums of independent random variables, convolution of random variables, order statistics of continuous random variables, covariance and correlation of random variables, and expected value and variance of sum of random variables have been explained. The second part of this chapter has been devoted to the conditional distribution, conditional expected value, conditional variance, expected value by conditioning, and variance by conditioning. In the third part of the chapter, the moment generating function and characteristic function have been defined, and a list of moment generating functions has been provided for special random variables. The last part of the chapter included the limit theorems in probability including Strong Law of Large Numbers and Central Limit Theorem. The concepts have been illustrated with several examples and problems.