Define Positive Integer

The definition of positive integer is one of the most important topic in mathematics. Positive integer is always present after the zero in the number line. The symbol used for representing the positive integer is called as the " + ". All the mathematical operations are done using the positive integer. In this article, we are going to see about the positive integer with brief explanation and some example problems.

Explanation to Define Positive Integer
The explanation for to define the positive integer is given below the following,

Addition problem for defining the positive integer
Subtraction problem for defining the positive integer
Multiplication problem for defining the positive integer
Division problem for defining the positive integer

Example Problems to Define Positive Integer

Example 1: Add the following positive integer, 36 and 24

Solution:

36 and 24

3 6

2 4

___

6 0

___

Result: Positive integer addition = 6 0

Thus, this is the result to define the addition problem problem of positive integer.

Example 2: Subtract the following to define positive integer, 36 and 24

Solution:

36 and 24

3 6

2 4

___

1 2

___

Result: Positive integer subtraction = 1 2

Thus, this is the result to define the subtraction problem of positive integer.

Example 3: Multiply the following to define positive integer, 36 and 24

Solution:

36 and 24

3 6

2 4

____

8 6 4

____

Result: Positive integer multiplication = 6 0

Thus, this is the result to define the multiplication problem of positive integer.


Example 4: Divide the following to define positive integer, 48 and 6

Solution:

48 and 6

6 ) 4 8 ( 8

4 8

____

0

____

Result: Positive integer division = 6 0

Thus, this is the result to define the division problem of positive integer.
Practice Problems to Define Positive Integer

Example 1: Add the following positive integer, 42 and 14.

Answer: 56

Example 2: Subtract the following positive integer, 42 and 14.

Answer: 28

Example 3: Multiply the following  positive integer, 42 and 14.

Answer: 588

Example 4: Divide the following positive integer, 56 and 7.

Answer: 6

Probability Distribution Definition

The word probability and chance are familiar to everyone. Many a time we come across statements like “It is possible that our school students may get state ranks in forthcoming public examination.

“Probably it may rain today”

Definition: The word chance, possible, probably, likely etc. convey some sense of uncertainty about the occurrence of some events. Our entire world is filled with uncertainty. We make decisions affected by uncertainty virtually every day. In order to think about and measure uncertainty, we turn to a branch of mathematics is called as probability.

Probability Distribution Definition-classical Definitions

Definition: If there are n exhaustive, likewise exclusive and in the same way likely outcomes of an experiment and m of them are favorable to an event A, and then the mathematical probability of A is defined as the ratio m/n.

Definition for random variable:

The outcomes of an experiment are represented by a random variable if these outcomes are numerical or if real numbers can be assigned to them. For example, in a die rolling experiment, the corresponding random variable is represented by the set of outcomes {1, 2, 3, 4, 5, 6} ; while in the coin tossing experiment the outcomes head (H) or tail (T) can be represented as a random variable by assuming 0 to T and 1 to H.

Types of Random variables:

(1) Discrete Random variable
(2) Continuous Random variable


Definition for Discrete Random Variable: If a random variable takes only a finite or a countable number of values, it is called a discrete random variable.

Example:
1. The number of heads obtained when two coins are tossed is a discrete random variable as X assumes the values 0, 1 or 2  which form a countable set.
2. Number of Aces when ten cards are drawn from a well shuffled pack of 52 cards.
Probability Distribution Definition-theoretical Distributions:

Theoretical probability distributions is classified into

1. Binomial Distribution

2. Poisson Distribution

3. Normal Distribution

4. Exponential Distribution

Multiplication Of Exponents

Exponents are significant in scientific notation, when large or small quantities are denoted as powers of 10. exponents are mentioned by superscripts, as in the examples above. But it is not always possible way to write them this method.  If x is the exponent to which is a minimum base quantity a is increased value, then a x can be written in ASCII as a power of x. In a scientific notation, the higher case letter E can be used to point out that a number is raised up to a positive or negative power of 10. For model take 125x3. Here 125 is coefficient of variable 'x’ Then 3 is the exponent value of x . Exponent value also known as power value.
Suitable Examples for Multiply Exponents


Exponents of 1 and 0
If the exponent is 1, then only have the variable itself (example a1 =a)

Generally need not to write the "1", but it sometimes helps to remember that y is also a1
Exponent of  0

If the exponent is 0, then the values are not multiplying by anything and the result is just "1" (example a0 = 1)
Multiplying Variables with Exponents

multiply this variable with exponents:

(z2)(z3)

So that z2 = zz, and z3 = zzz so that all the multiplies,

(z2)(z3)

= zzzzz

That is 5 "z"s multiplied mutually so the new exponent must be 5:

(z2)(z3)

= z5

The exponents say to that there are two "z"s multiplied by 3 "z"s for a total of 5 "z"s:

(z2)(z3)



= z2+3 =z5

So, the simplest method is to just add the components
Mixed Variables for Multiply Exponents:

Have a mix of variables:

Example 1:

=xy2z y3z

=x y2+3z1+1

=xy5z2

so the result is =x3y5z2    

Example 2:

=x3y3z3   x2yz

=x3+2 y3+1 z3+1

=x5y4z4

so the result is =x5y4z4

With constant examples:

Example 1:

=5xyz 4xyz

=(5 4)x1+1 y1+1 z1+1

=20x2y2z2

The result is =20x2y2z2

Example 2:

=7xyz 3 x2yz

=(73 ) x1+2y1+1z1+1

=21x3 y2z2

The result is  =21x3 y2z2