Please, answer if you are sure your answer is correct. Provide detailed solutions.

A pharmaceutics company considers undertaking research and development of a new drug. However, the outcome of R&D is uncertain. First, the firm only knows that a market value X of a patent for a new drug is uniformly distributed between 0 and 1 billion euros. Second, the firm does not know how costly R&D is. The cost of R&D depends on the difficulty of the research described by random variable Y uniformly distributed between 0 and 2. Given the difficulty, the cost of R&D is Y² billions euros. Assume that X and Y are independent.

1. What is the probability that R&D will result in a negative profit for the firm (assume that the firm sells the patent for its market value)?

2. Find CDF of profit.

3. How would you compute the expected profit and its variance (just give the formulas)?