The Area Under A Parametric Curve
Suppose and are the parametric equations of a curve. Then the area bounded by the curve, the -axis and the ordinates and will be Now I’ll solve some examples of that. EXAMPLE 1 According…
Formulas In Differentiation Applications
Suppose is the equation of any curve. So here are the first two formulas. EQUATIONS OF THE TANGENT AND THE NORMAL TO ANY CURVE The equation of the tangent of this…
Root Mean Square Value Of A Function
Suppose is the equation of a curve. Then the root mean square (rms) value of the function between ad will be Now I’ll give some examples of that. EXAMPLE 1 According to Stroud…
Length Of Any Curve
Let’s suppose is the equation of any curve. Then the length of the curve between and is EXAMPLE 1 According to Stroud and Booth (2013)*, “Find the length of the arc of the…
Nonhomogeneous Poisson Processes
Non-homogeneous Poisson process model (NHPP) represents the number of failures experienced up to time t is a non-homogeneous Poisson process {N(t), t ≥ 0}. The main issue in the NHPP model is…
Homogeneous Poisson Process
The poisson process is one of the most important and widely used processes in probability theory. It is widely used to model random points in time or space. In this article we…
Probability Distributions Set 3 (Normal Distribution)
The previous two articles introduced two Continuous Distributions: Uniform and Exponential. This article covers the Normal Probability Distribution, also a Continuous distribution, which is by far the most widely used model for continuous…
Probability Distributions Set 2 (Exponential Distribution)
The previous article covered the basics of Probability Distributions and talked about the Uniform Probability Distribution. This article covers the Exponential Probability Distribution which is also a Continuous distribution just like…
Probability Distributions Set 1 (Uniform Distribution)
1. Discrete Probability Distribution – If the probabilities are defined on a discrete random variable, one which can only take a discrete set of values, then the distribution is said to be…
Law of total probability
Prerequisite – Random variables, Conditional probabilityGiven n mutually exclusive events A1, A2, …Ak such that their probabilities sum is unity and their union is the event space E, then Ai ∩ Aj=…
