Expected Value from a Distribution Interview Questions
Expected value from a distribution interview prep for weighted averages, probability tables, continuous intuition, and sanity checks.
Candidates connecting distribution tables, density intuition, and expected value.
Expectation is a probability-weighted average
Once a distribution is known, expected value averages possible values using their probabilities as weights.
Discrete table setup
For a table, multiply each value by its probability and add the results. Check that probabilities sum to 1 before trusting the calculation.
Concrete example
If X equals 0 with probability 0.25 and 4 with probability 0.75, then E[X] = 0 x 0.25 + 4 x 0.75 = 3.
Continuous intuition
For continuous variables, expectation is still a weighted average, but weights come from density over intervals rather than point probabilities.
Sanity checks
The expectation should lie between the smallest and largest possible values when the variable is bounded. Units should match the variable.
Common mistakes
Candidates often average values without using probabilities. Equal averaging is valid only when the listed outcomes are equally likely.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.