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Is there a way to show $$\lim\limits_{x \to -\infty}xT_{\nu}(x)=0$$ where $T_{\nu}(x)$ is the CDF of Student's t distribution? Repetitive application of L'Hospital's rule to the fraction $\frac{x}{1/T_{\nu}(x)}$ does not work.

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Let me give you a hint.

While x/(1/F(x)) doesn't work, does F(x)/(1/x) work?

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  • $\begingroup$ It works! Thank you! $\endgroup$ – Alex May 22 at 23:56

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