Discrete Probability Distribution

A probability distribution for a random variable describes how probabilities are distributed over the possible values of the random variable.

Summary measures of a probability distribution are mean (central tendency), Variance (dispersion or spread) and Skewness or Kurtosis (shape).

$$X: {x_1, x_2 … x_n}$$ $$P: {p_1, p_2 … p_n}$$ $$Mean=E(X)= µ_x=\sum_{i=1}^n p_i x_i $$ $$Variance= Var(X)= σ_x^2=\sum_{i=1}^n p_i (x_i-µ_x)^2= \sum_{i=1}^n p_ix_i^2-µ_x^2 $$

The relationship between mean and variance for linear functions is:

$$Y=α+βX$$ $$E(Y)= α+βE(X)$$ $$Var(Y)= β^2 Var(X)$$

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.