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A class has 15 students whose ages are ...

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.

Text Solution

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Below mentioned is the table of `P(X)`
By using above data the we can find the mean and mean, variance and standard deviation of X.
Mean X = `E(X)=sum X_i P(X_i)=`
`=14xx2/15+15xx1/15+16xx2/15+17xx3/15+18xx1/15+19xx2/15+20xx3/15+21xx1/15`
by solving we will get `263/15 =17.53`
`E(X^2)=sum (X_i)^2 P(X_i)`
`=14^2xx2/15+15^2xx1/15+16^2xx2/15+17^2xx3/15+18^2xx1/15+19^2xx2/15+20^2xx3/15+21^2xx1/15`
by solving we will get `4683/15 =312.2`
`"Variance(X)" =E(X^2)-(E(X))^2`
`312.2-(263/15)^2`=`4.78`
`"Standard Variance"=sqrt("Variance")=sqrt(4.78)=2.186`
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