Mixture Distribution Interview Questions
Mixture distribution interview prep for hidden states, weighted distributions, total probability, total expectation, and variance cautions.
Candidates practicing latent-state, total probability, and total expectation prompts.
Hidden-state distributions
A mixture distribution appears when a hidden state chooses which component distribution generates the outcome.
Weight the components
Each component is weighted by the probability of its hidden state. The overall probability of an event is the weighted sum of component probabilities.
Concrete example
If a fair coin chooses between a fair die and a die that always rolls 6, the probability of rolling 6 is 0.5 x 1/6 + 0.5 x 1.
Expected value
The overall expectation is the weighted average of conditional expectations under each component. This is total expectation in distribution form.
Variance caution
Mixture variance includes both within-component variance and variation between component means. Do not just average variances unless the means match.
Common mistakes
Candidates often average outcomes instead of averaging probabilities or expectations with the correct hidden-state weights.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.