Problems for Cumulative Distribution Function

Earlier we discussed the introduction of a continuous random variable and cumulative distribution function. Please see this article if you haven’t read it about already. Now we will give some problems related to Cumulative distribution function so you can have a deeper understanding of this topic. These problems are adapted from the following textbook: “Probability and Random Processes by Scott Miller 2nd Edition.” Problem-1: Which of the following mathematical functions could be the CDF of some random variable? Remember: To be a CDF of some random variable, the function \(F_{X}(x)\) must start at zero when \(x = -\infty\), end at one...

Practice Problems (Introduction to Probability Theory)

A few practice problems related to Probability theory are given here. These problems are adapted from the textbook: Probability and Random Processes by Scott Miller 2nd Edition. These problems cover the following topics: Experiments, Sample spaces, events, Axioms of Probability, Assigning Probability, Joint and Conditional Probability, Independence, Baye’s Theorem, Total Law of Probability, Discrete Random variables. Problem-1: A roulette wheel consists of 38 numbers (18 are red, 18 are black, and 2 are green). Assume that with each spin of the wheel, each number is equally likely to appear. (a) What is the probability of a gambler winning if he...