Answer
Mean = 5
Variance = 6.66667
Standard Deviation = 2.582
Work Step by Step
Define the probability distribution:
$P(X=x)=\frac{1}{9},x=1,2,...,9$
Since there are 9 possible digits (1 to 9) and each is equally likely:
Mean = μ = ∑X * P(X)
= (1*1/9)+(2*1/9)+(3*1/9)+(4*1/9)+(5*1/9)+(6*1/9)+(7*1/9)+(8*1/9)+(9*1/9)
= 5
Variance = $ σ ^{2}$ = ∑[$X ^{2}$ * P(X)] - $ μ ^{2}$
=[ $1 ^{2}$ *1/9 +$2 ^{2}$ *1/9 + $3 ^{2}$ *1/9 + $4 ^{2}$ *1/9 + $5 ^{2}$ *1/9+ $6 ^{2}$ *1/9+ $7 ^{2}$ *1/9+ $8 ^{2}$ *1/9+ $9 ^{2}$ *1/9 ] -$ 5 ^{2}$
=31.66667-25
=6.66667
Standard Deviation = σ = $ \sqrt σ ^{2}$ = $\sqrt 6.66667$ = 2.582
