Probability Book Recommendation, Applied/Measure theory

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I just finished a course in probability theory in my undergrad but I felt that it lacked some things. So I'm looking for a good probability theory book for a second approach. One of the things the course lacked was a motivation for any of the definitions for the random variables. Especially the normal distribution. I have no idea why the curve is defined the way it is. So a book that went into the motivation and properties and applications of specific random variables would be great. It would also be nice if the book had a good measure theoretical basis, not some thing to in-depth, I have read some measure theory from Rudin. I know that both applied and measure theory might be too much to ask for from one book, so I value more the applied side.