so i have a problem which can be formulated in the following way: assume you have n particles and you know the initial position of each. There is some probability distribution P which contains the probability of having a particular velocity. Now, each particle has this same probability distribution of velocities. now choose some particle X and assume all other particles are moving toward X (for now we can assume X is still). In some time t, what is the expected number of collisions that X will have? well, i know you can compute it by saying prob of s (s goes from 0 to n) particles hitting X and find expected value that way. but this requires a lot of computation. eg. if you want to compute prob of 1 particle hitting X, you need to compute probability of particle 1 hitting X and none others hitting X, or probability of particle 2 hitting and none others, or probabilty of particle 3, etc. and these all differ since they are at different places. is there some type of better way to formulate this?