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# Machine Learning -III

Posted on 11th May 2019

### Normal Distribution:

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}

http://www.z-table.com/

### Probability Distribution

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

### Poisson Distribution

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

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