# ENG EC 381 Lecture Notes - Lecture 5: Probability Mass Function, Random Variable, Reliability Engineering

## Document Summary

Probability of failure when p1 and p2 are probabilities of components failures. Series connection: e events of system works. P[e] = p[ e1 and e2] = p[e1]p[e2] = (1 - p1)( 1 p2) < min { (1 - p1), ( 1 p2)} P[e] = 1 p[ec] = 1- p1 p2 1 - pi. C ] = p1 p2 n e2) c. Discrete random variables: a random variable is a mapping that assigns a number to an outcome, conventions: Random variable is usually a capital letter e. g. a. A value taken by a random variable is usually the lower case counterpart e. g. a. S = {a, b, c, d, f} Q = grade points associated with the grade. A probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value. Standard random variables: important families of random variables. X is a binomial (n, p) random variable if: