The article discusses conditional distributions and expectations, focusing on how variables relate to each other. It introduces new ways to calculate probabilities for both discrete and continuous data. The study shows that for continuous variables, the conditional density function is like the conditional probability mass function. It also explains how to find the conditional expectation and variance, which are important in statistics. The bivariate normal distribution is highlighted for its unique properties, such as having normal marginal and conditional distributions. Overall, the research explores how different variables interact and how to calculate their probabilities in various scenarios.