# What does “s” represent in the solution of this stochastic problem?

http://i.stack.imgur.com/LZPmN.png

My concern is what does s represent on the equation i circled?Is it the amount of Penalty he received or the number of ticket Harry get in order to achive 50 dollars of penalty? "s" raise to 50 power doesn't make sense to me, wouldn't the output would be very large if the s is equal to 2?

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So far as I can see, it’s simply the indeterminate in the probability-generating function. – Brian M. Scott Feb 20 '13 at 2:43

That appears to be the variable for the generating function. This is defined to be $$m_X(t) = E(e^{tX}).$$ It appears he is using $s$ instead of $t$.