ISYE 2027 Chapter Notes - Chapter 7: Probability Mass Function, Probability Distribution, Probability Density Function

• School: Georgia Tech
• Department: Industrial & Systems Engr
• Course: ISYE 2027
• Professor: All

Document Summary

Definition: the expectation of a continuous random variable x with probability density function f is the number: e. ii. Graphical representation of how the expected value can be considered a. Center-of-gravity e. iii: the expected value may not always exist: if then there is no expected value while if then we say the expected value is infinite, 7. 2: three examples, the geometric distribution a. i. In a lottery scenario, the expected amount of weeks until you win the lottery can be determined via a geometric distribution a. ii. The expectation of a geometric distribution: let x have a geometric distribution with parameter p; then: the exponential distribution b. i. In the chemical reactor example previously mentioned, the residence time has an exponential distribution b. ii. The expectation of an exponential distribution: let x have an exponential distribution with parameter ; then: the normal distribution c. i. The expectation of a normal distribution: let x be an distributed: 7. 3: the change of variable formula random variable.