Conversion : Binomial distribution --> Poisson Distribution. --> Gaussian distribution
Conversion : Binomial distribution --> Poisson Distribution. --> Gaussian distribution
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Event : Coin tossing
Trials : N
Outcomes : Head - H and Tail - T.
Probability : PH and PT ➔ Total probability, PH + PT=1.
Binomial distribution for N-trials : ( PH + PT)=∑x [N!/(x! (N-x)!)] (PH)x (1-PH)N-x = 1
Probability of getting x-number of Head from N-trial : Prob(x) = [N!/(x! (N-x)!)] (PH)x (1-PH)N-x
We plot Prob(x) with respect to x for different values of N and PH.
For PH=1/2, when N increases (i.e., "No. of trails" of the in the animated plot) the distrubution changes from Poisson to Gaussian.
Observations :
When no. trials is small (say, less than 5), the Binomial distribution close to Poisson distribution.
When no. trials becomes large (say, greater than 15), the Binomial distribution becomes Gaussian distribution.
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