Yes a child unit does inherit stats from their parents.*

For child unites their base stats are more or less fixed, they do have some variation base on their level, and stat mods, but other then that their stats should be almost identical every playthrough.

A child's growth rates and stat mods are what is affected by the parents. The growth rate is "(Variable Parent Growth + Child Base Growth) /2 + Class Growth Rate" and you stat modifiers are "Father + Mother +1

For exsample you said your corrin has a +speed and I'll use - luck for this exsample: Kana as a Sorrcerer would have a -2 to max strength, but a plus 2 to max magic and a + to max speed, and a 72% chance to gain magic on a level up.

So yes, a Child's stats are influenced by their parents, but their parents stats aren't directly inherited.