Answer
Mean:
$μ_X=4$
Standard deviation:
$σ_X=1.414$
Work Step by Step
Mean:
$μ_X=Σ[x.P(x)]=0\times P(0)+1\times P(1)+2\times P(2)+3\times P(3)+4\times P(4)+5\times P(5)+6\times P(6)+7\times P(7)+8\times P(8)=0\times0.003906+1\times0.03125+2\times0.1094+3\times0.2188+4\times0.2734+5\times0.2188+6\times0.1094+7\times0.03125+8\times0.003906=4$
Standard deviation:
$σ_X=\sqrt {Σ[x^2.P(x)]-μ_X^2}=\sqrt {0^2\times P(0)+1^2\times P(1)+2^2\times P(2)+3^2\times P(3)+4^2\times P(4)+5^2\times P(5)+6^2\times P(6)+7^2\times P(7)+8^2\times P(8)-4^2}=\sqrt {0\times0.003906+1\times0.03125+4\times 0.1094+9\times0.2188+16\times0.2734+25\times 0.2188+36\times0.1094+49\times0.03125+64\times0.003906-16}=1.414$
