Poisson Distribution

The Poisson distribution or Poisson law of small numbers is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event.

On of the Poisson distribution examples are mortality of infants in a city, the number of misprints in a book, the number of bacteria on a plate, and the number of activations of a geiger counter.

The poisson distribution calculator is the best way to tackle the problems under Poisson distribution. The Poisson distribution can be derived as a limiting case of the Binomial Distribution.

TYPES OF FUNCTIONS

The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output).

A function assigns a unique value to each input of a specified type.

Functions can be classified according to the properties they have. These properties describe the functions behaviour under certain conditions.

There are different types of functions.

Aggregate functions, datatype conversion functions , date functions, Mathematical functions, security functions, string functions, system functions, text and image functions.

Continuous function simply means that function is continuous without any abrupt or sudden change in the value of function. A function is continuous in its domain D if it is continuous at every point of its domain. Continuous functions are precisely those groups of functions that preserve limits.

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CIRCLE PROPERTIES

A circle is a simple shape of Euclidean Geometry consisting of those points in a plane which are equidistant from a given point called the center. The common distance of the points of a circle from its center is called its radius.

Listed below are some of the circle properties.

Center: A point inside the circle. All points on the circle are equidistant (same distance) from the center point.

Radius: The radius is the distance from the center to any point on the circle. It is half the diameter.

Diameter: The distance across the circle. The length of any chord passing through the center. It is twice the radius.

Circumference: The circumference of the circle is the distance around the circle.

Area: Strictly speaking a circle is a line, and so has no area. What is usually meant is the area of the region enclosed by the circle.

Chord: A line segment linking any two points on a circle.

Tangent: A line passing a circle and touching it at just one point is known as the tangent circles.

Secant: A line that intersects a circle at two points.

Linear Programming

Linear programming (LP) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear equations. Linear programming can be applied to various fields of study. It is used most extensively in business and economics, but can also be utilized for some engineering problems.

Linear programming is a considerable field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. The standard form of the linear programming problem is used to develop the procedure for solving a general programming problem.


Linear programming Constraints exist because certain limitations restrict the range of a variable's possible values. A constraint is considered to be binding if changing it also changes the optimal solution. Less severe constraints that do not affect the optimal solution are non-binding.

Important steps used while solving linear programming problems(LPP):-

Step 1: Interpret the given situations or constraints into inequalities.

Step 2: Plot the inequalities graphically and identify the feasible region.

Step 3: Determine the gradient for the line representing the solution (the linear objective function).

Step 4: Construct parallel lines within the feasible region to find the solution.

VOLUME OF A CONE FORMULA

A cone is a three dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex. it is the solid figure bounded by a plane base and the surface formed by the locus of all straight line segments joining the apex to the perimeter of the base.

The volume of a cone formula is as follows:-

Volume = 1/3Πr2h

Right Cone: A right cone is a cone in which the vertex is aligned directly above the center of the base. The base need not be a circle here.

A pyramid with a circular base. If the point (vertex) is directly above the centre of the circle, it is known as a right circular cone. A right circular cone is generated by rotating an isosceles triangle about its lines of symmetry. The distance from the edge of the base of a cone to the vertex is called the slant height.

Oblique Cone: When the vertex of a cone is not aligned directly above the center of its base, it is called an oblique cone

DIVISION ON FRACTIONS

Division on fractions is extremely easy. You just have to remember the rule to follow, and not get it confused with any other rule. You also have to remember to not do any "cross-canceling" until you have converted your division problem to multiplication as described below.

There is more than one method of dividing fractions. The easiest and most commonly taught way is to “invert and multiply.”To divide 2 fractions multiply the dividend by the reciprocal of the divisor.

Listed below is Dividing fractions examples:

(4/5) / (2/3) = (4/5) * (3/2)

(4/5) * (3/2) = (12/10)

12/10 = 1(1/5)

This is the quickest technique to divide fractions. The top and bottom are being multiplied by the same number and, since that number is the reciprocal of the bottom part, the bottom becomes one. Dividing anything by one leaves the value “anything” the same.

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GRAPH THEORY

Graph Theory is the study of graphs mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices.

Another important concept in graph theory is the path graph theory, which is any route along the edges of a graph. A path may follow a single edge directly between two vertices, or it may follow multiple edges through multiple vertices.

Below is one solved problem on Graph Theory:

Define a graph G such that V (G) = {3, 4, 5, 6, 12, 13, 14, 15} and two vertices ‘V’ and ‘A’ are adjacent if and only if GCD {V, A} = 1. Draw a figure of G and locate its size e(G).

Soultion:

The Graph theory answers for the above graph theory problem is e(G) = 21.