Denote by f(xi,yi), f is called the joint probability distribution function of (X,Y).
The concept of independent events leads quite naturally to a similar definition for independent random variables.
Two random variables X and Y are said to be independent if$$P(X=x,Y=y) = P(X=x).P(Y=y)$$
Roughly speaking, X and Y are independent if knowing the value of one does not change the distribution of the other.
Thus, if X and Y are independent, then:$$E(XY) = E(X)E(Y)$$
It follows that if X and Y are independent, then$$Cov(X ,Y)= 0,\,or \,Corr(X,Y) = 0 $$
Dependent variables may also be uncorrelated, if the relationship is non-linear, a u-curve for instance.
Use the Search Bar to find content on MarketingMind.
In an analytics-driven business environment, this analytics-centred consumer marketing workshop is tailored to the needs of consumer analysts, marketing researchers, brand managers, category managers and seasoned marketing and retailing professionals.
Is marketing education fluffy too?
Marketing simulators impart much needed combat experiences, equipping practitioners with the skills to succeed in the consumer market battleground. They combine theory with practice, linking the classroom with the consumer marketplace.