Calculating the Min Entropy of a string of bits Let's say you are looking to collect some randomness from your computer. At a given time stamp, you can always collect the following 16bits as part of the time stamp:


First 5 bits are fixed and always the same
The next 4 bits are not perfectly random and exhibit a probability of 1/8 for the different possibilities
Finally the last 7 bits are perfectly random, always


What would be the min entropy of one time stamp?

My intuition thinks the min entropy would be 3 bits (from the 4 imperfect bits) + 7bits from the last section, giving Min Entropy = 10 bits for one time stamp. Does this make sense?

EDIT: Rephrased the 2nd bullet point
If your probabilities are exact, then your math is right. But even if they are off by the slightest amount (e.g. $2^{-10000}$), it doesn't hold any more. For a practical system like timestamps in a computer, it's quite unlikely that your have exact values for the probabilities. If those probabilities are average measurements, then the resulting entropy is also only an average and not a lower bound (minimum).