Template:ProbabilityEquations

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  • PROBABILITY OF EXACT SEQUENCE (e.g. HHHHTT)
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  • P(x) = (p^k) * ((1-p)^(n-k))
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  • BINOMIAL RANDOM VARIABLE (BERNULLI)
  • ANY SEQUENCE (e.g. 'K' HEADS IN 'N' FLIPS)
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  • P(x) = choose(n,k) * (p^k) * ((1-p)^(n-k))
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  • BAYES
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  • P(A¡B) = P(B¡A)*P(A) / [P(B¡A)*P(A) + P(B¡~A)*P(~A)]
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  • Bayes theorem is used for testing conditional probabilities when we know the
  • probability of the occurence of event A, and the probability of the occurence
  • of event B given that event A has already occurred.
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  • PMF Probability Mass Function
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  • PMF is for descrete non-continuous variables
  • PMF is a general case for Bernoulli, and can be used for Bernoulli
  • The PMF for the variable X is denoted px
  • If x is any possible value of X, px(x) = P({X = x})
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  • PMF = [(factorial(n)) / ( (factorial(*a) * factorial(*b) * factorial(*c) )] *
  • [P(A^*a) * P(B^*b) * P(C^*c)]
  • given that x is a single observation from set X
  • where n is total number of x sampled from set X
  • where *a is x observations from group A of set X
  • where *b is x observations from group B of set X
  • where *c is x observations from group C of set X
  • where P(A^*a) is the probability of group A to the *a
  • where P(B^*b) is the probability of group B to the *b
  • where P(C^*c) is the probability of group C to the *c
  • and so forth for {A,B,C,...}
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  • Geometric Random Variable (GRV)
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  • The GRV is the number of X coin tosses needed for a head to come up for the first time
  • defined as px(k) = the probability of x for the k-ith toss
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  • px(k) = ((1-p)^(k-1)) * p
  • where p is the probability of flipping Heads on a coin
  • where x is the event of getting a Heads
  • where k is the number of flips
  • where 1-p is the probability of Tails
  • where k is the number of flips up to, and including, the first success
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  • Poisson Random Variable (PRV)
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  • Use Poisson to calculate PMF when P is really small and N is really big
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  • (exp(-(n*p))) * (((n*p)^k) / factorial(k))
  • where n = the number of trials
  • where p = probability of H
  • where k = the number of successful hits of H
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  • Sij
  • Sij = x2
  • 1 − e²
  • ±
  • ×
  • ÷

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