# 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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