Question

State whether the following is True or False :

If f(x) = k x (1 – x) for 0 < x < 1 = 0 otherwise k = 12

Options

• True

• False

Answer 1

False
Since the function represents a p.d.f. 1

∴ `int_0^1 f(x)*dx` = 1

∴ `int_0^1 "k"x (1 - x)*dx` = 1

∴ `"k" int_0^1 (x - x^2)*dx` = 1

∴ `[x^2/2 - x^3/3]_0^1 = (1)/"k"`

∴ `(1)/(2) - (1)/(3) = (1)/"k"`

∴ `(1)/(6) = (1)/"k"`

∴ k = 6.