Discrete Probability Distribution
- mean = μ = ∑[x · p(x)] = E(x) = expected value of x
- variance = sd^2 = ∑[(x-μ)^2 · p(x)]
[Binomial]
Binomial Probability Distribution
- E(x) = μ = n·pi
- Var(x) = sd^2 = n·pi(1-pi)
- concerned with an experiment that has only two possible outcomes.
- Given # of trials(n) and the probability of success, we want to find the probability that x number of success will happen.
- eg., head, tail / success, failure / ...
Parametres of Binomial Distribution
- n : number of trials
- pi : probability of success
Combination
- Used to count r object combinations from a set of n object.
- nCr = n! / r!(n-r)!
Binomial Probability - Probability Distribution Function
- f(x) = nCx · pi^x · (1-pi)^(n-x) for x = 0,1,2,...,n
[Poisson]
Poisson Distribution
- E(x) = lambda = μ
- Var(x) = sd^2 = lambda
- Given average number(lambda) of occurances in a specified interval, we want to find the probability that x number of occurances will happened during that interval.
Parametres of Binomial Distribution
- lambda: average number of occurences in a specified interval.
The Poisson approximation of the Binomial distribution
- In binomial, when pi is very small and n is large at the same time, the probabilities(P(x)) of the two distributions are very close.
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