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.

Explanation

According to question ,
There are 15 students in the class. Each student has the same chance to be chosen.

Therefore, the probability of each student to be selected is `frac{1}{15}.`

The given information can be compiled in the frequency table as follows.


`P(X=14)=frac{2}{15}, P(X=15)=frac{1}{15}, P(X=16)=frac{2}{15}, P(X=10)=


frac{3}{15}, P(X=18)=frac{1}{15}, P(X=19)=frac{2}{15}, P(X=20)=frac{3}{15}, P(X=21)=frac{1}{15}`

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