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प्रश्न
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.
बेरीज
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उत्तर
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`
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