exercise:D704fed4c7: Difference between revisions
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with <math>\alpha > 1 </math>. Determine the limit of the covariance of <math>X</math> and <math>Y</math> as <math>\alpha \rightarrow 1 </math>. | with <math>\alpha > 1 </math>. Determine the limit of the covariance of <math>X</math> and <math>Y</math> as <math>\alpha \rightarrow 1 </math>. | ||
< | <ul class="mw-excansopts"> | ||
<li>-0.0525</li> | <li>-0.0525</li> | ||
<li>-1/12</li> | <li>-1/12</li> | ||
| Line 16: | Line 16: | ||
<li>0.0525</li> | <li>0.0525</li> | ||
<li>0.1775</li> | <li>0.1775</li> | ||
</ | </ul> | ||
Latest revision as of 00:38, 17 March 2024
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