Probability Density vs Mass Function in Interviews
Probability density vs mass function interview prep for discrete PMFs, continuous PDFs, point probabilities, and interval probabilities.
Candidates switching between discrete and continuous probability.
PMF for discrete values
A probability mass function assigns probabilities to individual discrete values, such as die rolls or binomial counts.
PDF for continuous values
A probability density function describes continuous probability over intervals. Density is not the same thing as probability at a point.
Point probability contrast
For a continuous variable, the probability of one exact point is usually zero. For a discrete variable, a single point can have positive probability.
Concrete example
A fair die has P(X = 3) = 1/6. A uniform variable on [0, 1] has P(X = 0.3) = 0, but P(0.2 <= X <= 0.5) = 0.3.
Interview workflow
First identify whether the variable is discrete, continuous, or mixed. Then choose mass probabilities or interval-density reasoning.
Common mistakes
Candidates often read a density height as a probability. For continuous variables, probability comes from area over an interval.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.