L06.4 Conditional PMFs & Expectations Given an Event  Summary and Q&A
TL;DR
Conditional probability models involve revising probabilities based on new information, including conditional PMFs and expectations.
Questions & Answers
Q: What is a conditional probability model?
A conditional probability model involves revising probabilities based on new information. It uses conditional PMFs to represent the revised probabilities of events.
Q: How does a conditional PMF differ from an ordinary PMF?
A conditional PMF is similar to an ordinary PMF but applies to a new or revised conditional model. The entries in a conditional PMF still sum to 1, but the probabilities are conditional probabilities.
Q: How is the conditional mean of a random variable calculated?
The conditional mean of a random variable is calculated using the conditional probabilities. It is defined the same way as in the original case, but the calculation involves the conditional PMF.
Q: How does conditional probability affect the variance of a random variable?
In a conditional probability model, the variance of a random variable can change. If there is less uncertainty in the conditional model, the variance will be smaller compared to the original model.
Summary & Key Takeaways

Conditional probability models involve revising probabilities based on new information.

In a conditional probability model, the PMF is changed to a conditional PMF.

The conditional mean and variance of a random variable are calculated using conditional probabilities.