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YouTube is a Google service and you need to sign in with a Google account. This is a global account that

works with all Google’s tools, so if you change the email address to which notifications are sent, it will change them globally for every notification from every Google service.

To do this, click the account picture in the top-right corner of the YouTube homepage and click the gear icon to go to settings. Select Notifications on the left and look toward the bottom of the page for the address to which notifications are sent. Click the ‘Google+ notification settings’ link and find your email address in the ‘Notification delivery’ section. If your Hotmail address isn’t there, click ‘Add email address’ and enter it. 

You can then select an email address to which all notifications will be sent. If you don’t want to have all your

Google notifications rerouted, and only want to bounce your YouTube emails from your Gmail address, you could set up a filter. Log into Gmail and open one of the YouTube emails. Click the More button and choose ‘Filter messages like these’. The From filter should already be filled in. Click the ‘Create filter with this search’ link, tick the box next to ‘Forward it to’ and click the ‘add forwarding address’ link, if your Hotmail address isn’t already listed. Select it and click ‘Create filter’.