If the function f defined by f(x)=K (x-x² ) if 0 < x < 1=0 , other wise is the p.d.f. of a r. v. X , then the value of P (X < 1 2 ) is

Step-by-step solution

Given f to a the p.df of a r.v.x. aligned & f(x) d x=1 ₀¹ K (x-x² ) d x=1 & K [ x² 2 - x³ 3 ]₀¹=1 K ( 1 2 - 1 3 )=1 K 6 =1 K &=6 & P (x < 1 2 )= ₀^ 1 2 6 (x-x² ) d x= [ 6 x² 2 ]₀¹- [ 6 x³ 3 ]₀¹ &= [3 x²-2 x³ ]₀^ 1 2 = 3 4 - 2 8 = 3 4 - 1 4 = 1 2 aligned