“a pair of variables” and “mixture of Gaussian models”, why in the first sentence `a` is correct while is not required in the second sentence?

Question

As I mentioned in my previous question, a is a determiner used with a noun. However, I am confused about the usage of a in the following sentences.

Let (x_1, x_2) be a pair of variables.

The second sentence is wrong. Why?

We fit a mixture of Gaussian models.

I think the first sentence is correct. That is because a refers to the word pair, not the variables. However, the second sentence is wrong. Someone told me that I should not use a as we have the word models which is plural. I am really confused why a in the second sentence refers to models and not to mixture.

Answer 1

I agree with you. The article should normally refer to the noun right after it, as in the second sentence, "mixture".

The only possibility is that mixture should not be used with "the". But that's not the case. See this example sentence from Cambridge Dictionary on the entry "mixture":

Their latest CD is a mixture of new and old songs.

Therefore, I believe that you are right that the second sentence is correct.