# L06.4 Conditional PMFs & Expectations Given an Event | Summary and Q&A

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April 24, 2018
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L06.4 Conditional PMFs & Expectations Given an Event

## TL;DR

Conditional probability models involve revising probabilities based on new information, including conditional PMFs and expectations.

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### 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.