Answer to Question #301545 in Statistics and Probability for Lukas

Question

The proportion of assignments completed within a given day is described by the probability density function f (x) = 12(x - x^3 ) for 0 ≤ x ≤ 1. Find the expected proportion of completed assignments [4 marks].

Answer 1

we define the expected proportion as

$\int$ ₀¹ x * 12( x-x³) dx

solving the above integral, we obtain

12 ( x³/3 - x⁵/5 )¹₀

which equals 12 ( 1/3 - 1/5 )

which equals 12( 2/15 ) = 1.6