Joint Probability Distribution

Joint probability is the probability of two events happening together, and their joint probability distribution is the corresponding probability distribution on all possible outcomes of those events.

The joint probability distribution function of (X,Y) is denoted by f(xi,yi).

The concept of independent events extends to a similar definition for independent random variables. Two random variables X and Y are said to be independent if:

$$P(X=x,Y=y) = P(X=x).P(Y=y)$$

In simple terms, 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.

Previous     Next

Use the Search Bar to find content on MarketingMind.

Marketing Analytics Workshop

Marketing Analytics Workshop

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.

Digital Marketing Workshop

Digital Marketing Workshop

Unlock the Power of Digital Marketing: Join us for an immersive online experience designed to empower you with the skills and knowledge needed to excel in the dynamic world of digital marketing. In just three days, you will transform into a proficient digital marketer, equipped to craft and implement successful online strategies.