Herer, `S={TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}.`
`therefore" "n(S)=8.`
So, every single outcome has a probability `(1)/(8).`
Let X=number of heads in tossing three coins.
The number of heads may be 0, 1, 2, or 3.
So, the possible values of X are 0, 1, 2, 3.
`P(X=0)=P("getting no head")=P(TTT)=(1)/(8).`
`P(X=1)=P("getting 1 head")=P(TTH or THT or HTT)=(3)/(8).`
`P(X=2)=P("getting 2 heads")=P(THH, HTH, HHT)=(3)/(8).`
`P(X=3)=P("getting 3 head")=P(HHH)=(1)/(8).`
Thus, we have the following probability distribution.
`therefore" mean", mu=Sigmax_(i) p_(i)=(0xx(1)/(8))+(1xx(3)/(8))+(2xx(3)/(8))+(3xx(1)/(8))=(3)/(2).`
Variance, `sigma^(2)=Sigmax_(i)^(2)p_(i)-mu^(2)`
`=[(0xx(1)/(8))+(1xx(3)/(8))+(4xx(3)/(8))+(9xx(1)/(8))-(9)/(4)]=(3)/(4)`
Standard deviation, `sigma=(sqrt(3))/(2).`
