# DIFFERENCE BETWEEN DISCRETE AND CONTINUOUS RANDOM VARIABLES Discrete Random Variable :

If a random variable takes only a finite or countable number of values, it is called as discrete random variable.

Continuous Random Variable :

If a random variable takes all possible values between certain given limits, it is called as continuous random variable.

## Examples

Discrete Random Variable :

Let a coin be tossed ten times.

If "X" be the random variable and it stands for no. of heads, what possible values can "X" take?

X  =  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

If we get tail in all the ten times, then X = 0

If we get head one of the ten tosses and tails in the remaining 9 tosses, then X  =  1.

If we get heads two of the ten tosses and tails in the remaining 8 tosses, then X  =  2.

In this way, we get 11 values for "X" (from 0 to 10)

Here the random variable "X" takes 11 values only.

Because "x" takes only a finite or countable values, 'x' is called as discrete random variable.

Continuous Random Variable :

Already we know the fact that minimum life time of a human being is 0 years and maximum is 100 years (approximately)

Interval for life span of a human being is [0 yrs, 100 yrs]

If "X" be a random variable and it stands for life time of a human being, what possible values can "X" take ?

Then, X ∈ [0 yrs, 100 yrs]

Some possible values of "X" in [0 yrs, 100 yrs] are given below.

X = 3 years 2 weeks 4 days 5 hours 3 minute and 5 seconds.

X = 43 years 1 weeks 2 days 4 hours 3 minute and 15 seconds.

X = 89 years 3 weeks 5 days 6 hours 5 minute and 2 seconds.

X = 99 years 0 weeks 4 days 1 hour 19 minute and 45 seconds.

As we have written above, can we say all the possible values for "X" in the interval [0 yrs, 100 yrs]

Because we have infinite number of values for "X" in the interval [0 yrs, 100 yrs].

Because "X" takes all possible values in the interval [0 yrs, 100 yrs],  "X" is called as continuous random variable.

## Some More Examples

Discrete Random Variable :

1. No. of heads, in tossing 2 coins thrice.

2. No. of aces, when 10 cards are drawn from a well shuffled pack of 52 cards.

3. No. of doctors among the students who are in final years of the school

4. Getting 4's, when 5 dice are thrown once.

Continuous Random Variable :

1.  The life length in hours of a certain bulb.

2. "ph" value of a chemical compound which is randomly selected.

3.  Wages of workers in factory

4. Height of students in a university Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 