# Three numbers are selected at random (without replacement) from first six positive integers. Leo, find the mean and variance of the distribution. - Mathematics

Sum

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.

#### Solution

X = larger of of three numbers

X = 3, 4, 5, 6

P(x=3)=6xx1/6xx1/5xx1/4=1/20

P (x = 4) = 18xx1/6xx1/5xx1/4=3/20

P (x = 5) = 36xx1/6xx1/5xx1/4=6/20

P (x = 6) = 60xx1/6xx1/5xx1/4=10/20

 Xi Pi PiXi PiXi2 3 1/20 3/20 9/20 4 3/20 12/20 48/20 5 6/20 30/20 1 50/20 6 10/20 60/20 360/20

"Mean"=sumP_iX_i=(105/20)=5.25

sumP_iX_i^2=567/20

Var(X)= sumP_iX_i^2-(sumP_iX_i)^2

=567/20-(105/20)^2=0.787

Concept: Mean of a Random Variable
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