"Benim bir cevabım yok."

Sure. It's usually for situations where there might be many answers, and you have none. ("I don't have THE answer" implies that there's one answer, or one best answer.)

This is particularly common with open-ended questions, as sainio says. For example, if someone asks why something happened, you could say "I don't have an answer to that."

In Turkish you show the possesion with both the possessive suffix and possessive pronouns. To make it easier to understand explanation i'll make odd sentences.

have: sahip olmak

Ben bir cevaba sahip değilim.:I don't have an answer.

Ben cevabıma sahip değilim.:I don't have my answer.

If we wanted to compare the sentences it would look something like that. But you wouldn't say such a thing, just tried to show the difference.

"Benim cevabım değil."

Because they are different letters.

https://en.wikipedia.org/wiki/Close_back_unrounded_vowel ı

https://en.wikipedia.org/wiki/Close_front_unrounded_vowel i

"I have no an answer" is not a grammatically correct English sentence. You would say "I don't have an answer."

Turkish structures this thought using the possessive (my) , which is a little different from the way we do it with the nominative (I). It's almost like you're saying, "There isn't my answer" or "My answer doesn't exist."

'yok' doesn't mean 'have'. It means 'there isn't/aren't', 'doesn't exist', 'absent'. So this structure literally means 'There isn't my answer' or 'My answer doesn't exist.'. So since it is 'my answer' the translation should be '(benim) cevabım'.