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Add Solutions Chapter 1 & 2 #4

Closed julprat closed 2 months ago

julprat commented 2 months ago

Solutions needed for Exercises:

1.1 and 2.3, 2.4, 2.5, 2.6, 2.8

I have included some hints on where to find the solutions.

Please check the solutions that I have added for the other exercises.

Add your inputs to the update branch and send me a pull request once ready.

bmuuu98 commented 2 months ago

Files uploaded to a new branch "Sep19_Update".

julprat commented 2 months ago

In the proof of Exercise 2.3, I don't understand : we have $g\left(x{\theta}\right) = \left(1-\theta\right)g\left(x{1}\right) + \theta g\left(x{2}\right)$. I guess you mean $g\left(x{\theta}\right) \in \Gamma\left(x_{\theta}\right)$?

Also, I believe that you forgot to mention the assumption that $f(.)$ is concave. Also, you might need to state the space of (weakly?) concave functions is closed.

Exercise 2.5, point 2: Showing that the counterexaample of point 1 does not work is not enough, no? You also need to prove that there is no counterexample. Here you can use the answer to 2.4, point 1.

bmuuu98 commented 2 months ago

I have revised the answers to the questions mentioned above. Thank you!