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One would use the word **probability **in their day-to-day conversation and many people would have a clear-cut idea about its importance. Today, probability has become a key tool in statistics. In an actual scenario, both probability and statistics go hand in hand and it is impossible to discuss statistics without learning about the importance of probability. This is the one that would interpret the statistical results. Many statistical procedures would need decisions that would be based on the samples obtained and how these are affected randomly. By using probability theory, one can express the inevitable things in the decisions. This theory is a branch of mathematics that would analyze the probability of random happenings. The main concepts in probability theories are stochastic processes, events, and random variables.

Advanced **Probability Theory** is the key concept in statistics that comprises various important topics like Laplace transforms measure-theoretic probability theory, discrete probability distributions, continuous probability distributions, central limit theorem, etc. Some of the important concepts and theorems include Kolmogorov Consistency theorems, conditional expectations, Radon-Nikodym Theorem, and discrete parameter martingales.

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Measure Theoretic Probability | Bayes' Rule |

Applied Probability | Independence of Random Variables |

Fluctuations in Coin Tossing and Random Walks | Conditional Probabilities |

Joint and Conditional Distributions | Occupancy and Matching Problems |

Heuristics in Judgment and Decision-Making | Probability Theory |

Probability Axioms | Normalizing Constant |

Random Variables | Combinatorial Probability |

Probability Spaces and Probability Measures | Transformation of Variables |

Convergence of Random Variables | Probability Spaces |

Probability Theorems | Probability Theories |

Distribution of random variables | Set Theory |

Binomial & Poisson Distribution | Metric Spaces |

Conditional Probability | Bayes Theorem |