What is true about (Behavioral) Finance?

Assume you are offered to play a lottery that pays $0 with a probability of 0.9 and $1,000 with a probability of 0.1 (Option A). Your second option is to receive a certain amount of $100 (Option B). What option would you choose if you were risk-averse (without knowing the precise utility function)?

Recall the mean posterior belief from the Normal-Normal-Model of Bayesian Updating:
 $s\cdot\frac{\frac{1}{\sigma^2}}{\frac{1}{\sigma^2}+\frac{1}{\tau^2}}+\mu_0\cdot\frac{\frac{1}{\tau^2}}{\frac{1}{\sigma^2}+\frac{1}{\tau^2}}$ 
 What is the meaning of the term
 $\frac{\frac{1}{\sigma^2}}{\frac{1}{\sigma^2}+\frac{1}{\tau^2}}$  ?

In class, you learned about mispricings resulting from spin-offs. What possible reasons can explain this phenomenon?

Bonus Question (Level: Hard)

Firm A plans to spin off its wholly owned subsidiary, Firm B. Stockholders of A will receive 1.5 shares of B for each share of A. After the IPO of B, the following market prices are observed:

A: $80 B: $70

What is the correct "stub value"?