Plotting a distribution over time

I would like to clarify the meaning of 'plotting a distribution over time' for the following scenario or similar:

We have $k$ players playing a game in which they accumulate points. At each time $t$, each player $i$ holds some amount of points $s_i$, so we could have a distribution $X_t(s)$ of point levels achieved by these $k$ players at $t$. As the game goes on, we record $X_t(s)$ at each $t$, and at the end, we are asked to "plot $X_t(s)$ over time".

What exactly does this mean by plotting a distribution such as $X_t(s)$ over time? Thanks.

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Perhaps, you could plot the pdf/cdf as a series of curves- one curve for each time period. The x-axis would be the number of points and the y-axis would represent the number (for pdf)/cumulative total(for cdf) of players for each point. Perhaps, that is what is meant by the plot of X_t(s) over time? –  tards Nov 9 '11 at 1:21
@tards, thanks for your comments. I was thinking along that line but as the number of time steps may be large, then there would be almost too many curves on the graph. Is it possible to plot just one curve and use time step $t$ as the x-axis? –  balllib Nov 9 '11 at 10:56