In quantum mechanics, probability amplitudes determine the interference patterns observed in experiments.

To analyze a discrete random variable, we often examine its probability mass function to determine the probability assigned to each possible value.

To estimate the probability density function of the experimental measurements, we applied kernel smoothing to the sample data.

In the lecture, the professor compared several probability mass functions to demonstrate how different discrete distributions allocate probability across outcomes.

Researchers compared the probability density functions of the two datasets to identify differences in shape and spread.

The conditional probability distribution of the test score given study time revealed that students who studied longer were much more likely to score above 80.

Conditional probability distributions are essential for modeling dependencies between random variables in Bayesian networks.

The banking team prioritized the high probability trade, allocating extra resources to ensure a smooth closing.

The fund manager focuses on high probability trades to protect capital during volatile markets.