Bradley Monk: Created page with " ---------------------------------------- * PROBABILITY OF EXACT SEQUENCE (e.g. HHHHTT) ---------------------------------------- * P(x) {{=}} (p^k) * ((1-p)^(n-k)) *------..."

2013-07-17T06:23:02Z

Created page with " *----------------------------------------* * PROBABILITY OF EXACT SEQUENCE (e.g. HHHHTT) *----------------------------------------* * P(x) {{=}} (p^k) * ((1-p)^(n-k)) *------..."

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*----------------------------------------*
* PROBABILITY OF EXACT SEQUENCE (e.g. HHHHTT)
*----------------------------------------*
* P(x) {{=}} (p^k) * ((1-p)^(n-k))
*----------------------------------------*

*----------------------------------------*
* BINOMIAL RANDOM VARIABLE (BERNULLI)
* ANY SEQUENCE (e.g. 'K' HEADS IN 'N' FLIPS)
*----------------------------------------*
* P(x) {{=}} choose(n,k) * (p^k) * ((1-p)^(n-k))
*----------------------------------------*

*----------------------------------------*
* BAYES
*----------------------------------------*
* P(A¡B) {{=}} P(B¡A)*P(A) / [P(B¡A)*P(A) + P(B¡~A)*P(~A)]
*----------------------------------------*
* 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.
*----------------------------------------*

*----------------------------------------*
* PMF Probability Mass Function
*----------------------------------------*
* 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})
*----------------------------------------*
*
* 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,...}
*----------------------------------------*

*----------------------------------------*
* Geometric Random Variable (GRV)
*----------------------------------------*
* 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
*----------------------------------------*
*
* 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
*----------------------------------------*

*----------------------------------------*
* Poisson Random Variable (PRV)
*----------------------------------------*
* Use Poisson to calculate PMF when P is really small and N is really big
*----------------------------------------*
*
* (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
*----------------------------------------*

* {{math|S<var>ij</var>}}
* {{math|S<var>ij</var> {{=}} <var>x</var>2}}
* {{math|{{radical|1 − ''e''²}}}}
* −
* ±
* ×
* ÷
* &frasl;
}}

Template:ProbabilityEquations - Revision history

Bradley Monk: Created page with " *----------------------------------------* * PROBABILITY OF EXACT SEQUENCE (e.g. HHHHTT) *----------------------------------------* * P(x) {{=}} (p^k) * ((1-p)^(n-k)) *------..."

Bradley Monk: Created page with " ---------------------------------------- * PROBABILITY OF EXACT SEQUENCE (e.g. HHHHTT) ---------------------------------------- * P(x) {{=}} (p^k) * ((1-p)^(n-k)) *------..."