Answer
Mean:
$μ_X=7.2$
Standard deviation:
$σ_X=1.2$
Work Step by Step
Mean:
$μ_X=Σ[x.P(x)]=0\times P(0)+1\times P(1)+2\times P(2)+3\times P(3)+4\times P(4)+5\times P(5)+6\times P(6)+7\times P(7)+8\times P(8)+9\times P(9)=0\times0.000000512+1\times0.00001843+2\times0.0002949+3\times0.002753+4\times0.01652+5\times0.06606+6\times0.1762+7\times0.3020+8\times0.3020+9\times0.1342=7.2$
Standard deviation:
$σ_X=\sqrt {Σ[x^2.P(x)]-μ_X^2}=\sqrt {0^2\times P(0)+1^2\times P(1)+2^2\times P(2)+3^2\times P(3)+4^2\times P(4)+5^2\times P(5)+6^2\times P(6)+7^2\times P(7)+8^2\times P(8)+9^2\times P(9)-7.2^2}=\sqrt {0\times0.000000512+1\times0.00001843+4\times0.0002949+9\times0.002753+16\times0.01652+25\times 0.06606+36\times0.1762+49\times0.3020+64\times0.3020+81\times0.1342-51.84}=1.2$
