A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.


Given: The class of 15 students with their ages.

Form the given information we can draw a table:


X



14



15



16



17



18



19



20



21



f



2



1



2



3



1



2



3



1



P(X = 14)


P(X = 15)


P(X = 16)


P(X = 17)


P(X = 18)


P(X = 19)


P(X = 20)


P(X = 21)


Hence, the required probability distribution is,


X



14



15



16



17



18



19



20



21



P(X)



















Therefore E(X) is:





⇒ E(X) = 17.53


And E(X2) is:





⇒ E(X2) = 312.2


Then Variance, Var(X) = E(X2) – (E(X))2


= 312.2 – (17.53)2


= 312.2 – 307.417 ≈ 4.78


And Standard deviation



⇒ Standard deviation ≈ 2.19


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