Learn Turkish: Ben yorgunum.

It is attached to the end of the word! In Turkish, words like "am", "is", or "are" usually appear as suffixes (endings) on the noun or adjective. The ending -um on yorgunum is the "am" that matches "I".

Why is the ending -um and not -im?

This happens because of 4-way vowel harmony. The suffix must match the last vowel of the word it attaches to. The base word for tired is yorgun, which has u as its last vowel. In 4-way harmony, if the last vowel is o or u, the suffix must use an u.

The lesson says the "I am" suffix is -(y)Im. Why is there no y here?

The y is a buffer letter that is only used when you need to prevent two vowels from touching. Because the word yorgun ends with a consonant (n), there is no vowel crash. Therefore, we don't need the buffer letter and can attach the -um directly.

Do I need to include the word Ben if the ending already means "I am"?

No, you can just say Yorgunum. Because the -um ending specifically means "I am", the pronoun Ben (I) is optional. Including it just adds a little bit of emphasis, like clarifying "I am tired."