Abstract
Abstract The distribution of a discrete random variable may be specified via its probability mass function. The key notion of independence for discrete random variables is introduced. The concept of expectation, or mean value, is defined for discrete variables, leading to a definition of the variance and the moments of a discrete random variable. Joint distributions, conditional distributions, and conditional expectation are introduced, together with the ideas of covariance and correlation. The Cauchy–Schwarz inequality is presented. The analysis of sums of random variables leads to the convolution formula for mass functions. Random walks are studied in some depth, including the reflection principle, the ballot theorem, the hitting time theorem, and the arc sine laws for visits to the origin and for sojourn times.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
