This is an introduction to discrete random variables. A baseball player has a .230 average. If he has 3 official at-bats, what is his probability of getting more than one hit? Over many games with 3 official at-bats, what is his average number of hits? Variance? Standard deviation? These questions can be answered through modeling using the probability mass function (PMF) f(x)=P(X=x) of the discrete random variable X = # of hits in 3 at bats. For simplicity, we need to assume the at-bats are Bernoulli trials that are identical and independent (binomial distribution). Then we can use the probability multiplication and addition rules to define f(x) and answer the questions. The mean (expected value) E[X] is also computed in a couple of ways. Moreover, the variance Var(X) and standard deviation σ are defined as measures of spread. Also of interest are properties of expectation as well as the geometric random variable X = # of at-bats until the first hit. amzn.to/3rjDOoA (Probability and Statistics with Applications: A Problem Solving Text, by Asimow and Maxwell)
Calculus-based Probability and Statistics for Engineers and Scientists, Lecture 5, Part 2. Also for Data Scientists and Actuarial Science majors.
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Негізгі бет Prob & Stats, Lec 5B: Introduction to Discrete Random Variables & Expected Value (Baseball Example)
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