The diameter , Say X , of a electric cable , is assumed to be continuous random variable with p.d.f : f(x)= 6x(1-x) , 0<=x<=1.

(1) Check that the above is a P.D.F.

(2) Obtain an expression for the c. d. f. of X.

(3) Compute P(X<=1/2| 1/3<=X<=2/3), and

(4) Determine the value of k such that P(X<k)=P(X>k).