Conditional probability: introdution of another variable

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SUMMARY

The discussion centers on the calculation of conditional probability P(A|C) using the formula involving summation over B, specifically P(A|B) * P(B|C). This approach requires specific conditions on the variables B to ensure the validity of the calculation. The participants emphasize the importance of understanding the underlying assumptions necessary for this formula to hold true in probability theory.

PREREQUISITES
  • Understanding of conditional probability concepts
  • Familiarity with the law of total probability
  • Knowledge of probability distributions
  • Basic mathematical skills for summation and manipulation of probabilities
NEXT STEPS
  • Study the law of total probability in detail
  • Explore the concept of independence in probability theory
  • Learn about Bayesian inference and its applications
  • Investigate the implications of conditioning on multiple variables
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Students of statistics, data scientists, and professionals in fields requiring probabilistic modeling and analysis.

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Consider the conditional probability P(A|C) .

Is it true that we can calculate above as

Summation over B P(A|B)*P(B|C) .
 
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You'll need some conditions on the Bi for that to be true
 

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