You are asked to evaluate the effort of a CEO in a firm. The CEO can take two effort levels, High and Low, but you cannot directly observe them. Based on the past observation, you are informed that he will take high effort level with probability .7. If he takes high effort, then the firm's earnings per share (EPS) would take three values $2, $1 and -$1 with probabilities .7, .2 and .1, respectively. However, if he takes low effort, then his firm's EPS would take three values $1, $0 and -$1 with probabilities .2, .3 and .5, respectively.

Please answer the following questions:

(1) What is the unconditional probability for each of the four EPSs?

(2)What is the (unconditional) expected value of the firm's EPS?

(3) If the CEO takes low effort, then what is the (conditional) expected EPS for the firm?

(4) What is the (unconditional) probability of EPS being less than $1? (5) If you observe that EPS is $1, then what is the probability of the CEO having taken high effort?