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Probability density function plays fundamental role in qunatum mechanics. I wanted to ask if there is any analogous density function in classical mechanics. Obviously if we solve Hamilton equations we get fully deterministic trajectory. But it should be possible to find function which shows probability of finding classical particle in given interval of space (or generalized coordinate). For example it is known that if we have got harmonic oscillator it is most probable to find it nearby farthest place from "0". Do you know how to construct such function? If yes, can we calculate avarage energy, momentum, possition etc. as we do it in qunatum mechanics (by integral)?