7. (15 points total). Consider a one-time, two potential outcome frameworks where there exists Company \\( Q \\) stock current selling for \\( \\$ 55 \\) per share and a riskless \\( \\$ 100 \\) face value T-bill currently selling for \\( \\$ 80 \\). Suppose Company \\( Q \\) faces uncertainty, in that it will pay its owner either \\( \\$ 30 \\) or \\( \\$ 75 \\) in 1 year. Further assume that the physical probability that the stock will drop is 0.2 . a. List the risk-neutral probabilities for this payoff space. b. Compute values for the Radon-Nikodym derivative for this change of measure. c. Value call and put options on this stock, with exercise prices equal to \\( X=60 \\). d. Does put-call parity hold for this example