Just one more thing, which isn't good in regards to authenticity, is that Marilyn never signed exactly the same way twice. So the likelihood of her signing just like her Fox contract on this photo is quite small. And no inscription. Pretty much every photo on Ebay which is just her signature is a forgery or reprint. She wrote inscriptions on most signings.
Also you can see the influence of a line underneath made this quite a tidy signing on her contract, but your photo has no line to sign on, yet she signed it the same? it doesn't make sense because without a guideline she wrote with a squiggly arc shape/baseline, if you know what I mean. Such as:
Can you see the details of the pen on the photo up close? because to my eye it resembles a reprint of her 20th Century Fox contract signature, which is the one that wound up being used as her official logo
I can't find another example where Marilyn has signed a photo with just her signature, except a small polaroid obviously written in a hurry. She always put some kind of inscription if signing photos and she didn't do it all that often, usually just for personal friends and collegues.