IF its not too much trouble could you explain how you solved for each bullet point

A continuous RV, x has probability distribution function (PDF) as defined below: p(x) = k x (x+1) for -asxs0 = k x (1 - x /2) for Osxs+b where k is a positive constant; and, a = 1.5 and b = 2.1 Determine the following: (i) Value of k (ii) Expected value, E[x] of the RV (iii) Second moment of the RV distribution (iv) Standard deviation of the RV distribution . Cumulative distribution function, Px(x)Multiple-choice Answers: Choose the Correct Result ii iii iv V Px(x ) = 1 0.729 0.482 0.375 0.378 k(x + a) + (k/2)(x2- a2) - asxs0 k(x- x2/4) Osxs+b Px(x)= 2 0.724 0.493 0.343 0.370 k(x + a) x (k/2)(x2 + a2) - asxso k(x + x2/4) Osxs+b Px(x)= 3 0.749 0.484 0.353 0.338 k(x + a) - (k/2)(x2 + a2) - asxs0 k(x + x2/2) O sxs +b Px(x)= 4 0.718 0.482 0.370 0.352 k(x + a) + (k/2)(x2 - a2) -asxs0 k(x- x2/4) Osxs+b Px(x ) = 5 0.722 0.485 0.365 0.355 k(x - a) - (k/2)(x2 + a2) -asxs0 k(x- x2/4) Osxs+b O Choice 1 O Choice 2 O Choice 3 O Choice 4 O Choice 5