Consider a user is uploading a set of files to a server. Assuming a bandwidth of $b$ bits/s, it takes $t_i=|f_i|/b$ seconds to upload the file, where $|f_i|$ is the size of file $i$. If the user does not report the file size to the server, from the server's perspective, the transmission time of the files, i.e, $t_i$, follow an exponential distribution. However, if the user report the file size before uploading the file, it doesn't follow exponential distribution anymore, because at least it doesn't have the memoryless property. How can such a situation be described?
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The distribution of an unknown quantity often changes depending on what information is available. This is an example of marginal and conditional distributions: without any knowledge of the file sizes, the marginal distribution of the time required to transfer each file is exponential. Conditional on knowing the file sizes, though, the distribution of time required changes drastically.
Here's another example: Suppose I tell you that I chose a point x somewhere on the globe, and I ask you to give me a probability distribution for the temperature at that location at noon local time tomorrow. Without knowing where that point is, your distribution will be fairly wide, with values from below freezing to up to maybe 45 degrees celsius--the location might be in either Alaska or Australia, after all. But if I then tell you that the location is in Australia, the distribution conditional on that information is much different--much more mass near 40 degrees and none below freezing.