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An investor plans to invest in two start-up companies. Each start-up has probability 0.30 of being...

An investor plans to invest in two start-up companies. Each start-up has probability 0.30 of being successful, and the success of each company is independent of the other. If either of the two start-ups is successful, it will generate $1 million in profit for the investor; if both are successful, net profits will be $1.8 million because of higher taxes. If neither is successful, profits will be 0. Let X be the investor’s profit (in $ million).

(a) What is the probability distribution of X? (Hint: what is the probability that none of the start-ups is successful? exactly one? both?)

(b) Find E[X]

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丛0.3 D 42 - \ E(x): $0.582 million

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