Abstract: Learning the joint probability of random variables (RVs) is the cornerstone of statistical signal processing and machine learning. However, direct nonparametric estimation for ...
Probability theory is like the crystal ball of mathematics, helping us predict the likelihood of events occurring. The magic number always lies between 0 and 1, inclusive, where 0 means “impossible” ...
Abstract: Consider a system comprising sensors that communicate with a remote estimator by way of a so-called collision channel. Each sensor observes a discrete random variable and must decide whether ...
The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. The chi-square distribution is often used in ...
In the early development of probability theory, only discrete random variables (although not called random variables at the time) were considered. Isaac Newton (1643-1727) considered the idea of ...
In a raffle with 20 tickets, 6 tickets are drawn for prizes. The first prize winner gets $\$20$, 2 second prize winners get $\$10$, and three third prize winners get $\$5$. What is the sample space ...
Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...
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