Answer
Mean:
$μ_X=1.8$
Standard deviation:
$σ_X=1.122$
Work Step by Step
Mean:
$μ_X=Σ[x.P(x)]=0\times P(0)+1\times P(1)+2\times P(2)+3\times P(3)+4\times P(4)+5\times P(5)+6\times P(6)=0\times0.1176+1\times0.3025+2\times0.3241+3\times0.1852+4\times0.05954+5\times0.01021+6\times0.000729=1.8$
Standard deviation:
$σ_X=\sqrt {Σ[x^2.P(x)]-μ_X^2}=\sqrt {0^2\times P(0)+1^2\times P(1)+2^2\times P(2)+3^2\times P(3)+4^2\times P(4)+5^2\times P(5)+6^2\times P(6)-1.8^2}=\sqrt {0^2\times 0.1176+1^2\times 0.3025+2^2\times 0.3241+3^2\times0.1852+4^2\times 0.05954+5^2\times 0.01021+6^2\times0.000729-3.24}=1.122$
