# What is the random variable?

**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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