What is the random variable?

timer Asked: May 20th, 2015

Question description

A machine has 100 identical components. The number of components that can break down during a shift follows a Poisson distribution with mean 5. The cost, in dollars, of servicing the machine at the end of each shift is given by the square of the number of components that broke down during that shift. Thus, if only one component broke down during the shift, it costs $1 to service the machine, if two components broke down, the cost of servicing the machine goes up to $4, with 3 components having broken down, the servicing cost is $9, and so on. What is the expected cost of servicing the machine at the end of a shift?
(Hint: Recall that variance equals E(X^2)-(E(X))^2, where X is the random variable. What is the random variable here?

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