Those who are free of resentful thoughts surely find peace. - Buddha
Posted on 11th May 2019
https://en.wikipedia.org/wiki/Normal_distribution
Normal or Gaussian or bell shaped curve distribution is a very common continuous probability distribution. Normal Distribution has bell shaped curve, it’s a symmetric single model distribution with highest density at and around the mean :
Ex. Age, Marks
f(x | mean, variance) = 1/sqrt(2*pi*variance) * exponent * ^((x - mean)^2/ 2*variance)
Some Important properties :
Mean = Median = Mode
Area within 1 Std. Dev around the mean ~ 68.3 %
Area within 2 Std. Dev around the mean ~ 95.4 %
Area within 3 Std. Dev around the mean ~ 99.7 %
Standard Normal Distribution and z Score/ z Statistic
Special case of Normal distribution with Mean = 0 and Variance = 1, Std. Deviation = 1. it has total area under the curve = 1 which represents probability.
f(x | mean, variance) = 1/sqrt(2*pi*1) * exponent * ^((x - 0)^2/ 2*1)
Any Normal distribution can be converted into Standard Normal Distribution by applying following transformation :
Z = (x - μ) / σ
{This is called as z Score, it tells us how many SD far we are from mean}
Binomial Distribution
Bi -> 2, Nomial -> Nominal -> Only 2 possible outcomes (Success or Failure)
When we perform any given experiment multiple times and we are interested in knowing #successes, this type of experiments are known as Binomial experiments, Ex. Flipping the coins multiple times. Using Binomial Distribution we can answer probability related questions for any Binomial experiments.
Probability of getting ‘x’ #Successes out of ‘n’ trials using Binomial Distribution –
P(x) = ncx Px (1-P)n-x ;
P = Probability of Success in 1 trial
Some Important properties :
N Fixed Number of Trials
Only 2 Possible Exclusive Outcomes
Probability of success remain same during the experiment
All the trials are independent
When we analyze the probability of occurrence of any event during some specified interval of time or according to some other binding conditions.
Probability of ‘x’ occurrence using Poisson Distribution –
P(x) = (lamda^x e-lamda )/x! ;
lamda = Mean/Expected #Occurrence Some Important properties :
All the occurrences are independent
Expected #Occurrence doesn’t change over the period of time
Good, better, best. Never let it rest. Untill your good is better and your better is best. - St. Jerome