Griffiths QM problem 4.28: Checking uncertainty principle for a spin state

In this video I will solve Griffiths QM problem 4.28, as it appears on the 3rd edition of the book. The goal is to check the uncertainty principle for a spin state.

My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Explaining the problem
01:30 Writing the state in dirac notation
02:14 Normalizing the state
03:40 Expectation value of Sx
05:20 Expectation value of Sx^2, Sy^2, Sz^2
07:15 Expectation value of Sy
09:30 Expectation value of Sz
11:00 Uncertainty of Sx
11:27 Uncertainty of Sy
14:15 Uncertainty of Sz
17:35 Checking the uncertainty principle for Sx, Sy
20:08 Checking the uncertainty principle for Sy, Sz
21:20 Checking the uncertainty principle for Sz, Sx
23:00 Recapping