If the following function is probability density function of r.v. X f(x) = kx^2(1-x) , for 0 < x < 1 = 0 , otherwise, then the value of k is

Step-by-step solution

For a function to be a probability density function, the total probability over its entire domain must be 1 . _ - ^ f(x) dx = 1 ₀¹ kx^2(1-x) dx = 1 k ₀¹ (x^2 - x^3) dx = 1 k [ x^3 3 - x^4 4 ]₀¹ = 1 k ( 1 3 - 1 4 ) = 1 k ( 4 - 3 12 ) = 1 k ( 1 12 ) = 1 k = 12 Answer: 12