PROBLEM 6. Goku is preparing for a battle with his rival Vegeta. Based on previous battles, when Goku has a power level of g and Vegeta has a power level of v, we can calculate the probability of Goku's victory with the formula: 8+v Let W be a random variable such that W = 1 if Goku wins and W = 0 if he loses (a) Calculate the PDF for W if Goku currently has a power level of g = 1,100 while Vegeta has a power level of v= 1,000. (b) Now suppose Goku's friends will revive him (to full power) with the Dragon Balls if he loses the first battle against Vegeta, but only once, as the Dragon Balls disappear for 1 year after use. Goku wants to secure favorable o.90 odds of winning overall, either by winning the first battle or losing the first but winning the second. If Vegeta starts with a power level of v = 1,000 for both battles (if necessary), what power level does Goku need to achieve Pr[W = 1] = 0.9?

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