Final answer:
In the sentence provided, 'their' is the correct pronoun to use because it serves as a gender-neutral, singular pronoun that agrees with the generic antecedent 'One of these students'.
Step-by-step explanation:
The correct pronoun that agrees with its antecedent in the sentence 'One of these students assembled their own computer.' is 'their.' This is because, in contemporary English, 'their' is often used as a gender-neutral, singular pronoun, which is suitable when the gender of the antecedent is collective, generic, or unknown. This approach helps avoid gender bias and makes the sentence inclusive, aligning with modern guidelines on pronoun-antecedent agreement.