Laboratory in Oceanography Data and Methods Correlation Analysis

Laboratory in Oceanography: Data and Methods Correlation Analysis MAR 550, Spring 2020 Miles A. Sundermeyer MAR 550 Spring 2020 1

Linear Correlation Analysis Review of Definitions The Cumulative Distribution Function (CDF) of the random variable x is the function Fx(x) satisfying: Sundermeyer MAR 550 Spring 2020 2

Linear Correlation Analysis Review of Definitions The Probability Density Function (PDF) of the random variable x is the function fx(x) satisfying: Sundermeyer MAR 550 Spring 2020 3

Linear Correlation Analysis Review of Definitions The Expectation or Expected Value of any function g(x): Examples: Process mean: Process variance: Sundermeyer MAR 550 Spring 2020 4

Linear Correlation Analysis Review of Definitions The Joint Cumulative Distribution Function of two random variables, x and y, is Fxy(x, y): Sundermeyer MAR 550 Spring 2020 5

Linear Correlation Analysis Review of Definitions The Joint Probability Density Function of two random variables, x and y, is a piecewise continuous function fxy(x, y) satisfying: Sundermeyer MAR 550 Spring 2020 6

Linear Correlation Analysis Review of Definitions Two variables, x and y, are Independent if Example: Sundermeyer MAR 550 Spring 2020 7

Linear Correlation Analysis Review of Definitions The Covariance of x and y is E((x-mx)(y-my)): Example: The covariance of two independent variables is zero Sundermeyer MAR 550 Spring 2020 8