Let [math]X[/math] be a random variable with the following density function:

[[math]] f(x) = 6x(1 - x), \quad \text{for } 0 \le x \le 1 [[/math]]

Suppose that [math]Y = \exp(\exp(X)) [/math], determine the mode of the distribution of [math]Y[/math].

• 2.7
• 3.9
• 5.2
• 6.4
• 7.8