"तुम्हारी बहन दौड़ रही है।"

Translation: Your sister is running.

[AJ72T]

This is the Continuous Present, using रहना (the verb 'to live') as the auxiliary verb, right?

[vinaysaini]

Yes. रहा है, रहे हैं, रही है, रहे हैं are the continuous tense endings of the verb रहना that express continuous aspect uncompleted actions. So रहना can also mean 'to remain' within the continuous state of an incomplete activity.

[Oxartum]

I was finding hard to keep in mind that «दौड़» = «run». However, I have researched a bit, and I have discovered this word is related to English words of Greek origin like «hippodrome» (racing circuit for horses), «drastic» (via «δρᾶσῐς» = «strength»), and drama (via «δράω» = «I take action»). Using the Germanic route instead, the same Indo-European root is related to the English word «trade» (via the Proto-Germanic «tradō» = «track, way»).

Isn't it amazing?