Define Random and Discrete Random Variable with Examples

what is Random Variable?

The word Random Variable is quite commonly used in our daily life. Table of Random numbers have desired properties no matter how chosen from the table by rows, columns, diagonal, or irregularly. The first such table was published by L.H.C. tippet in 1927. The Table of Random numbers contains digits 1,2,3…9. Most modern methods of selecting a sample are based on the theory of random selection. 
Discrete Random Variable and Continuous Random Variable are the types of Random Variable.

Define Random and Discrete Random Variable

According to a simple definition of Random number

“A random number is a numerical quantity whose value depends on chance.”

According to a proper definition of Random variable

“A Random variable is a set of values assigned to all possible outcomes of a random experiment.” A random variable can also be written as r.v. If we write A, B, C…F on the six faces of a die these letters are not Random variables but if we right some numerical values like 1,2,3,4,5,6 on six faces of the die, Then we have a set of values called Random variable. A distribution that gives probability to each value of the random variable is called a probability distribution. random variable also called a chance variable

Examples of Random Variable

  • The number of errors per page in a balance sheet
  • The height (in cm) of players of a basketball team
  • A countable number of values

Types of Random Variables

There are two types of Random variable

  • Discrete random variable
  • Continuous Random variable

Define Discrete Random Variable?

A random variable X that can assume finite or countably infinite or only some selected values in a given interval is called a discrete random variable. Its probability is denoted by p(x). Discrete probability function provides a probability for each value of the discrete random variable.

Examples of discrete random variable

  • The number of bacteria in 1cc of water
  • The number of fatal accidents
  • Number of tails obtained in the toss of four coins
  • Number of houses in a certain town

Define Continuous Random Variable?

A random variable X that can assume an unlimited number of variables in a given interval is called a Continuous Random variable. The probability density function provides probabilities for each value of a continuous random variable. It can be a formula or equation.

Examples of a continuous random variable

  • The price of a car
  • Weight of a person
  • Length of a bridge
  • The height of a person
  • The amount of rainfall

Properties of Random numbers

  • Random number is used to obtain the number of items in a population.
  • By using a random number table, even digits 0,2,4,8 will stand for head and odd digits 1,3,5 7,9 will stand for the tail.

Types of Functions with Definition

Most Important Types of functions are

Some important types are functions are given below:  

Types of Functions with Definition

Algebraic Function Definition Short

Algebraic function are those functions which are defined by algebraic expressions.

Linear functions Short Definition With Example

If the degree of polynomial function is 1, then it is called a linear function. linear function is of the form:

f(x) = ax + b (a not equal to 0) a, b, are the real numbers.

for example  f(x) = 3x + 4 or y = 3x + 4 is a linear function. its domain and range are the set of real number.

Identity of Trigonometric Functions

For any set X, a function I : X → X of the form I(x) = x ∀  x 𝛜 X, is called an identity function. its domain and range is the set X itself. in particular, if  X  = r then I(x) = x for all x 𝛜 R, is the identity function.

Constant Function Examples and Definition

Let X and Y be sets of real numbers. A function C : X  → Y defined by C(x) = a, ∀  x 𝛜 X , a 𝛜 Y and defined by is called a constant function. for example, C: R  → R defined by C(x) = 2 ,  ∀  x 𝛜 R is a constant function.  

What is Rational functions in Math?

A function R(x) of the form P(x)/Q(x), were both P(x) and Q(x) are polynomial functions and Q(x) ≠ 0 is called a rational function. The domain of a rational function R(x) is the set of all realm numbers x for which Q(x)  ≠ 0.