(Solved): A hypothetical small car ferry runs every hour from one side of a river to th ...

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A hypothetical small car ferry runs every hour from one side of a river to the other. Based on historical records, the number of vehicles \( \mathrm{V} \) on a randomly chosen ferry trip has probability distribution given in the table below. \( [\mathrm{V} \) You can confirm that it has expected value \( \mu_{V}=3.87 \) and standard deviation \( \sigma_{V}=1.286 \) (a) Let \( \mathrm{C}=5^{+} \mathrm{V} \) be the random variable for the amount of money collected on a randomly selected trip. \[ \mu_{C}= \] \[ \sigma_{C}= \] \[ \sigma_{C}^{2}= \] (b) Let the random variable \( \mathrm{P}=5^{\circ} \mathrm{V}-20 \) be the profit made by the ferry company on a randomly selected trip.