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Probability Theory

Oct 24, 2023

• event A
  • probability of event A occuring P(A)
• random variable X
  • probability distribution for random variable X
  • probability density function for X
  • expectation and variance of X
• $P(\text{sure event}) = 1$
• $P(\text{impossible event}) = 0$
• $P(A) + P(\neg{A}) = 1$, complementary events
• $P(A \vee B) = P(A) + P(B) - P(A \wedge B)$
  • A, B are exclusive events: $P(A \wedge B) = 0 \implies P(A \vee B) = P(A) + P(B)$
• $A\sube B \implies P(A) \leq P(B)$
• $A_1, A_2, …, A_n$ are elementary events $\implies \displaystyle\sum_{i=0}^n P(A_i) = 1$