"Difference between discrete and continuous random variables" is the basic stuff required for the students who would like to study theoretical distributions in probability.

The difference between discrete and conitnuous 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. **

Let us look at some detailed examples on "Difference between discrete and continuous random variables".

**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.

Since "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].

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

Let us look at some more examples to have better understanding on "Difference between discrete and continuous random variables"

**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

After having gone the stuff explained above, we hope that the students would have understood "Difference between discrete and continuous random variables".

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