You could use arithmetic operators + - * / directly between NumPy arrays, but this section discusses an extension of the same where we have functions that can take any array-like objects e.g. lists, tuples etc. and perform arithmetic conditionally. Arithmetic Conditionally: means that we can define conditions where the arithmetic operation should happen.

Used to describe probability where every event has equal chances of occuring.

Logistic Distribution is used to describe growth. Used extensively in machine learning in logistic regression, neural networks etc.

Multinomial distribution is a generalization of binomial distribution. It describes outcomes of multi-nomial scenarios unlike binomial where scenarios must be only one of two. e.g. Blood type of a population, dice roll outcome.

Exponential distribution is used for describing time till next event e.g. failure/success etc. It has two parameters: scale - inverse of rate ( see lam in poisson distribution ) defaults to 1.0. size - The shape of the returned array.

Chi Square distribution is used as a basis to verify the hypothesis. It has two parameters: df - (degree of freedom). size - The shape of the returned array.

Rayleigh distribution is used in signal processing. It has two parameters: scale - (standard deviation) decides how flat the distribution will be default 1.0). size - The shape of the returned array.

A distribution following Pareto's law i.e. 80-20 distribution (20% factors cause 80% outcome). It has two parameter: a - shape parameter. size - The shape of the returned array.

Zipf distritutions are used to sample data based on zipf's law. Zipf's Law: In a collection, the nth common term is 1/n times of the most common term. E.g. the 5th most common word in English occurs nearly 1/5 times as often as the most common word.

ufuncs stands for "Universal Functions" and they are NumPy functions that operate on the ndarray object.

Poisson Distribution is a Discrete Distribution. It estimates how many times an event can happen in a specified time. e.g. If someone eats twice a day what is the probability he will eat thrice?

There are primarily five ways of rounding off decimals in NumPy: truncation fix rounding floor ceil

NumPy provides functions to perform log at the base 2, e and 10. We will also explore how we can take log for any base by creating a custom ufunc. All of the log functions will place -inf or inf in the elements if the log can not be computed.

What is the difference between summation and addition? Addition is done between two arguments whereas summation happens over n elements.

To find the product of the elements in an array, use the prod() function.

A discrete difference means subtracting two successive elements. E.g. for [1, 2, 3, 4], the discrete difference would be [2-1, 3-2, 4-3] = [1, 1, 1] To find the discrete difference, use the diff() function.

The Lowest Common Multiple is the smallest number that is a common multiple of two numbers.

The GCD (Greatest Common Denominator), also known as HCF (Highest Common Factor) is the biggest number that is a common factor of both of the numbers.

NumPy provides the ufuncs sin(), cos() and tan() that take values in radians and produce the corresponding sin, cos and tan values.

NumPy provides the ufuncs sinh(), cosh() and tanh() that take values in radians and produce the corresponding sinh, cosh and tanh values.

A set in mathematics is a collection of unique elements. Sets are used for operations involving frequent intersection, union and difference operations

Splitting is reverse operation of Joining. Joining merges multiple arrays into one and Splitting breaks one array into multiple. We use array_split() for splitting arrays, we pass it the array we want to split and the number of sp

If you have Python and PIP already installed on a system, then installation of NumPy is very easy.

NumPy is used to work with arrays. The array object in NumPy is called ndarray. We can create a NumPy ndarray object by using the array() function.

Array indexing is the same as accessing an array element. You can access an array element by referring to its index number. The indexes in NumPy arrays start with 0, meaning that the first element has index 0, and the second has index 1 etc.

Slicing in python means taking elements from one given index to another given index

By default Python have these data types: strings - used to represent text data, the text is given under quote marks. e.g. "ABCD" integer - used to represent integer numbers. e.g. -1, -2, -3 float - used to represent real numbers. e.g. 1.2, 42.42 boolean - used to represent True or False. complex - used to represent complex numbers. e.g. 1.0 + 2.0j, 1.5 + 2.5

The main difference between a copy and a view of an array is that the copy is a new array, and the view is just a view of the original array. The copy owns the data and any changes made to the copy will not affect original array, and any changes made to the original array will not affect the copy. The view does not own the data and any changes made to the view will affect the original array, and any changes made to the original array will affect the view.

The shape of an array is the number of elements in each dimension

Reshaping means changing the shape of an array. The shape of an array is the number of elements in each dimension. By reshaping we can add or remove dimensions or change number of elements in each dimension

Iterating means going through elements one by one. As we deal with multi-dimensional arrays in numpy, we can do this using basic for loop of python. If we iterate on a 1-D array it will go through each element one by one.

Joining means putting contents of two or more arrays in a single array. In SQL we join tables based on a key, whereas in NumPy we join arrays by axes. We pass a sequence of arrays that we want to join to the concatenate() function, along with the axis. If axis is not explicitly passed, it is taken as 0.

NumPy is a Python library used for working with arrays. It also has functions for working in domain of linear algebra, fourier transform, and matrices. NumPy was created in 2005 by Travis Oliphant. It is an open source project and you can use it freely. NumPy stands for Numerical Python.

You can search an array for a certain value, and return the indexes that get a match. To search an array, use the where() method.

Sorting means putting elements in an ordered sequence. Ordered sequence is any sequence that has an order corresponding to elements, like numeric or alphabetical, ascending or descending. The NumPy ndarray object has a function called sort(), that will sort a specified array.

Getting some elements out of an existing array and creating a new array out of them is called filtering. In NumPy, you filter an array using a boolean index list. A boolean index list is a list of booleans corresponding to indexes in the array.

Random number does NOT mean a different number every time. Random means something that can not be predicted logically.

Data Distribution is a list of all possible values, and how often each value occurs. Such lists are important when working with statistics and data science. The random module offer methods that returns randomly generated data distributions.

A permutation refers to an arrangement of elements. e.g. [3, 2, 1] is a permutation of [1, 2, 3] and vice-versa. The NumPy Random module provides two methods for this: shuffle() and permutation().

Seaborn is a library that uses Matplotlib underneath to plot graphs. It will be used to visualize random distributions.

The Normal Distribution is one of the most important distributions. It is also called the Gaussian Distribution after the German mathematician Carl Friedrich Gauss. It fits the probability distribution of many events, eg. IQ Scores, Heartbeat etc. Use the random.normal() method to get a Normal Data Distribution.

Binomial Distribution is a Discrete Distribution. It describes the outcome of binary scenarios, e.g. toss of a coin, it will either be head or tails