PROBABILITY

PROBABILITY

1. Is a mathematical statement about the likelihood that it will occur. The sum of the probabilities of all possible outcomes of any event is

   • Theorem
     • Principle of Inclusion and Exclusion
       • P(X [ Y ) = P(X) + P(Y ) − P(X \ Y )
         • (PIE), we conclude that when two events are mutually exclusive, the probability that both of them will occur (P(A [ B)) is P(A) + P(B).
     • Independence Principle
       • the probability that both will occur is equal to the product of their individual probabilities. In other words, if A and B are independent
         • P(A \ B) = P(A) + P(B)
   • Random Variables
     • Random Variables
       • A variable that may take on different values depending on the outcome of some event.
         • probability distribution.
           • A list that gives the probability for each discrete value of a random variable
     • Expected Value
       • is the sum of the product of each possible value and its corresponding probability
         • E(X) = Σn i=1(xi · P(xi))
     • Variance and Standard Deviation
       • The variance 2 of a random variable, which takes on discrete values x and has mean μ, is given by the equation
         • 2 = (x − μ)2P(x) = (x2P(x)) − μ2