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Let X denote the sum of the numbers obta...

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

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Let x denote the sum obtained when two fair dice are rolled.
Thus, X can have values `2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.`
`=>P(X=2)=P(1,1)=1/36`
`=>P(X=3)=P{(1,2),(2,1)}=2/36​`
`=>P(X=4)=3/36`
`=>P(X=5)=4/36`
`=>P(X=6)=5/36 `
`=>P(X=7)=6/36 `
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