CustomerID AND CustomerEmail are both Candidate keys. (or minimal superkeys).
A superkey is any attribute (or collection of attributes) of a table that would ensure that each tuple (or row) in the table is uniquely identified.
The trivial superkey is all the attributes of the table (since you expect no two rows in the table to be exactly the same).
CustomerID is therefore a minimal superkey (ie. candidate key) since no two entries will have same customerID.
From the two candidate keys (CustomerID and CustomerEmail) you picked customerID to be the primary key.
Now all you have to do is look up the customerID and you are presented with their name, email, birthday and country. In other words all those things are dependent on customerID. (or the customerID determines the customerName).
However since customerEmail is also a candidate key, all these things are also dependent on customerEmail.