A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 20% chance of returning $5,000,000 prot, a 30% chance of returning $1,000,000 prot, and a 50% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 prot, a 35% chance of returning $1,000,000 prot, and a 45% chance of losing the million dollars. The third company, a biotech rm, has a 10% chance of returning $6,000,000 prot, a 60% of no prot or loss, and a 30% chance of losing the million dollars. (a) Construct a PDF for each investment. Enter the exact answers as fractions or decimals. :3 P(:c) 1,000,000 Number 5,000,000 Number Software Company \fa: P (w) 1,000,000 Number 1,000,000 Number 3,000,000 Number Hardware Company :r P (:13) 1,000,000 Number 0 Number 6,000,000 Number Biotech Firm (b) Find the expected value for each investment. Software company: $ Number Hardware company: $ Number Biotech firm: $ Number