A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X?
Note Many of the times while solving such simple problems we make a mistake in counting. So at first, we should make a frequency table which tells us no of students in the class of the same age.
This makes our interpretation easier.
∴ frequency distribution table for age and number of students is:
X represents the age of a random student.
∴ X can take values 14,15,16,17,18,19,20 or 21
Total No. of students in class = 15
Using the above frequency table, we can easily see a total number of students of a particular age, and hence we can find probability easily.
P(X = 14) = 
{As probability = 
}
Similarly,
P(X = 15) = 
; P(X = 16) = 
; P(X = 17) = 
P(X = 18) = 
; P(X = 19) = 
; P(X = 20) = 
P(X = 21) = 
Now we have pi and xi.
∴ Required probability distribution is:-
