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An insurance company offers you a contract for 150 dollars. There’s a 5\
  • Calculate the expected profit \(E(X)\) of the insurance company.
  • Explain what the result means in terms of the average expected profit for the company.
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  • Let \(X\) represent the gain of the insurance company. The probability distribution of \(X\) is
    \(x\) 150 -1850
    \(P(X=x)\) \(\frac{19}{20}\) \(\frac{1}{20}\)
    .
    \(E(X) = 150 \cdot \frac{19}{20} + (-1850) \cdot \frac{1}{20} = \frac{2850}{20} - \frac{1850}{20} = \frac{1000}{20} = 50\)
  • Since \(E(X) = 50\), we expect the insurance company to earn an average profit of \(\dollar 50\).
}