Question 1022893
We make use of the formula {{{Var(X) = E(X^2) - (E(X))^2}}}.
To find {{{E(X^2)}}}, we find pmf of {{{X^2}}}:
{{{X^2}}}        1     4      9      16      25
p({{{X^2)}}})  0.36   0.19  0.17    0.06    0.22

which is identical to the pmf of X.
==> {{{E(X^2) = 1*0.36+ 4*0.19 + 9*0.17 + 16*0.06 + 25*0.22 = 9.11}}}

Now E(X) = 0.36 + 2*0.19 + 3*0.17 + 4*0.06 + 5*0.22 = 2.59

==> {{{Var(X) = 9.11 - 2.59^2 = 2.4019}}}