SCIT

This is the repository for all SCIT tasks

Task 1

We are required to plot the histograms of Poisson and normal distributions for set of 1000 samples 3 times making use of the numpy.random.poisson() and the numpy.random.normal() functions to generate the samples and then, using the same parameters, select 100 data points at random and plot the histogram of the average of them.

Pre-requisites: python, matplotlib, numpy

Sub-Task 1: Plotting Poisson Distribution

A set of 1000 samples is selected randomly using the numpy.random.poisson() function. It takes the parameters lam and size which are the expectation of interval and the number of samples to be generated respectively and returns an array containing the samples from the poisson distribution. The size determines the output shape.

The graph is plotted using the pyplot.hist() function

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Inference: The numpy.random.poisson() function generates samples that follow the poisson distribution with highest frequencies around the mean value hence creating the same curve as a poisson distribution.

Sub-Task 2: Plotting Normal Distribution

A set of 1000 samples is selected randomly using the numpy.random.normal() function. It takes the parameters mean,standard deviation and size.

Mean: Expectation value of the distribution

Standard deviation: Spread or width of the distribution

Size: Determines the shape of the output

pyplot.hist() function is used to spawn the following graphs.

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Inference: The numpy.random.normal() function generates samples that follow the normal distribution with highest frequencies around the mean value hence creating the bell curve.

Sub-Task 3: Plotting the Average of Poisson and Normal Distributions

A set of 100 data points are selected randomly from both of the above two distributions using the numpy.random.poisson() and the numpy.random.normal() function. A histogram is plotted for the new data set generated taking the average of their respective datapoints from both the distributions.

pyplot.hist() function is used for the generation of the histogram.

Mean=100

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Inference: The mean of the average graph is very close to the mean of both the normal and poisson distributions, Which implies that the mean of the average histograph of both normal and poisson distribution still gives the same mean as the respective distributions itself.