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  • Three numbers are selected at random (without replacement ) from first six positive integers. Let X denote the largest of the three numbers obtained. Find the probability distribution of X. Also, find the mean and variance of the distribution.

Three numbers are selected at random (without replacement ) from first six positive integers. Let X denote the largest of the three numbers obtained. Find the probability distribution of X. Also, find the mean and variance of the distribution.

 

 

 

 
 
 
 
 

Answers (1)

As the first 6 positive integers are 1,2,3,4,5,6 so the variate X takes values 3,4,5 and 6. The probability distribution is given as :

X 3 4 5 6
P(X)

\frac{1}{20}

 \frac{3}{20} \frac{6}{20} \frac{10}{20}

 

Now the mean of the distribution \mu = \sum x p(x) = \frac{105}{20} = \frac{21}{4}

Variance of the distriburtion = \sigma ^2= \sum x^2 p(x) - \mu ^2 = \frac{567}{20}- \frac{441}{16} = \frac{2268-2205}{80}= \frac{63}{80} 

Posted by

Ravindra Pindel

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