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]

Everyone's answer will be "NO"

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

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