Find the value of a that nukes the following function a prob

Find the value of a that nukes the following function a probability density function f(x) = ax2(2 - x) for 0

By normality condition,

Intergal [ax^2 (2 - x)] |(0,2)

= a Intergal [2x^2 - x^3] |(0,2)

= a [2x^3 / 3 - x^4/4] | (0,2)

= a {[2(2^3)/3 - 2^4/4] - [2(0^3)/3 - 0^4/4]}

= a {4/3} = 1

Thusm

a = 3/4 = 0.75 [ANSWER]