Answer
Mean:
$μ_X=6.75$
Standard deviation:
$σ_X=1.299$
Work Step by Step
Mean:
$μ_X=Σ[x.P(x)]=0\times P(0)+1\times P(1)+2\times P(2)+3\times P(3)+4\times P(4)+5\times P(5)+6\times P(6)+7\times P(7)+8\times P(8)+9\times P(9)=0\times0.000003815+1\times0.0001030+2\times0.001236+3\times0.008652+4\times0.03893+5\times0.1168+6\times0.2336+7\times0.3003+8\times0.2253+9\times0.07508=6.75$
Standard deviation:
$σ_X=\sqrt {Σ[x^2.P(x)]-μ_X^2}=\sqrt {0^2\times P(0)+1^2\times P(1)+2^2\times P(2)+3^2\times P(3)+4^2\times P(4)+5^2\times P(5)+6^2\times P(6)+7^2\times P(7)+8^2\times P(8)+9^2\times P(9)-6.75^2}=\sqrt {0\times0.000003815+1\times0.0001030+4\times 0.001236+9\times0.008652+16\times0.03893+25\times 0.1168+36\times0.2336+49\times0.3003+64\times0.2253+81\times0.07508-45.5625}=1.299$
