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If x is the number of tails in three tos...

If x is the number of tails in three tosses of a coin, then determine the standard deviation of X.

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Given that, random variable X is the number of tails in three toses of the coin.
So, X=0,1,2,3.

`rArrP(X=x)=""^(n)C_(x)(p)^(x)q^(n-x)`
Where n=3,p`=1//2` andx=0,1,2,3

We know that, Var(X)=`E(X^(2))-[E(X)]^(2)`
where, `E(X^(2))=sum_(i=1)^(n)x_(i)^(2)P(x_(i))and E(X)=sum_(i=1)^(n)x_(i)P(x_(i))`
`therefore E(X^(2))=sum_(i=1)^(n)x_(i)^(2)P(X_(i))=0+3/8+3/2+9/8=24/8=3`
and `[E(X)]^(2)=[sum_(i=0)^(n)x_(i)^(2)P(x_(i))]^(2)=[0+3/8+3/4+3/8]^(2)=[12/8]^(2)=9/4`
`therefore Var(X)=3-9/4=3/4`
and standard deviation of X=`sqrt(Var(X))=sqrt(3/4)=sqrt3/2`
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