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A coin is tossed thrice. X denotes the n...

A coin is tossed thrice. X denotes the no. of heads appeared. Find the mean and variance of X.

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S={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
P(X=0)`=1/2xx1/2xx1/2=1/8`
P(X=1) `=1/2xx1/2xx1/2+1/2xx1/2xx1/2+1/2xx1/2xx1/2=3/8`
P(X=2) `=1/2xx1/2xx1/2+1/2xx1/2xx1/2+1/2xx1/2xx1/2=3/8`
P(X=3) `=1/2xx1/2xx1/2=1/8`

`E(X)=1/8xx0+3/8xx1+3/8xx2+1/8xx3=3/2`
`E(X^2)=1/8xx0+3/8xx1+3/8xx4+1/8xx9=3`
`Var(X)=E(X^2)-(E(X))^2`
`=3-9/4=3/4`
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