Applied Mathematics

Classification of Second Order Partial Differential Equations

If z is a function of two independent variables x and y. Then second order partial differential equation Rr+Ss+Tt+ f(x,y,z,p,q)=0 Where r, s and t are and R, S and T are continuous functions of…

Caley-Hamilton Theorem

To  understand  Caley-Hamilton theorem you have to know about characteristic polynomial. Characteristic Polynomial If A is a square matrix of of size n * n, and I is identity matrix of the same size as…

Logistic Regression

Hyperbolic Functions These functions are very important in regression, classification and to build neural networks. Moreover, it is important to remember expression hyperbolic functions in the form of exponential functions. I have written the expressions…

Linear Regression in Statistics

Linear regression Linear regression refers to find out degree of relationship between two variables in the form of a linear function y=mx+c using statistical techniques. Where m is gradient and c is intercept on y…

Poisson Distribution as a Limiting Case of Binomial Distribution

For large value of n binomial distribution asymptotically tends to Poisson distribution. Probability distribution  function of binomial random variable  is Probability distribution of Poisson random variable is Poisson Distribution as a Limiting Case of Binomial…

Exponential Probability Distribution

A random variable X is said to follow exponential distribution if it follows the following probability mass function. Exponential probability distribution is a continuous distribution. Probability Distribution Function of Exponentially Distributed Variable X   It…

Poisson Distribution in Statistics

A random variable X is said to follow Poisson distribution, if it follows the following probability distribution function. Poisson distribution is a discrete probability distribution. It models the following types of problems Find out number …

Central Limit Theorem and Normal Distribution

Why is normal distribution is important? To understand the question you have to go through the Central Limit Theorem. Central Limit Theorem According to central limit theorem if X1, X2, X3,……Xn are random variables…

Correlation in Statistics

Correlation Correlation measures  the relation between two variables  that how they are related.  And is denoted by r and  ρ moreover, the correlation quantifies the level of relationship between -1 to +1. If the value…

Skewness and Kurtosis

Skewness and Kurtosis- Introduction- Skewness and Kurtosis are very important  concepts in statistics and have several applications.  In addition, they characterize the nature of data distribution which make data analysis easier. Moreover, I will separately…