The variables [math]X[/math] and [math]Y[/math] have joint density function

[[math]] f(x,y) = \begin{cases} \frac{2(\alpha + 1)}{\alpha -1}, \quad 0 \leq x \leq 1, x^{\alpha} \lt y \leq x \\ 0, \quad \textrm{Otherwise} \end{cases} [[/math]]

with [math]\alpha \gt 1 [/math]. Determine the limit of the covariance of [math]X[/math] and [math]Y[/math] as [math]\alpha \rightarrow 1 [/math].

• -0.0525
• -1/12
• 0
• 0.0525
• 0.1775