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A student invests in three risky projects. He will spend $100 on each project. Let S1, S2 and S3 be the events that the first,

A student invests in three risky projects. He will spend $100 on each project. Let S1, S2 and S3 be the events that the first, second and third project respectively return some money. Suppose all events are mutually independent and p1=P(S1)=0.2 and S1 returns $1000, p2=P(S2)=0.3 and S2 returns $500, p3=P(S3)=0.6 and S3 returns $200. Let W be the random variable that represents the student's net returns in dollars.

  1. Calculate the possible values for W and the corresponding probabilities
  2. What is the expected value of the winnings, E[W] ?

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