Filling in the worksheet, we see that the new information does not in fact alter the odds, and the probability that the car is not behind door 1 remains at 2/3, so it is advantageous to switch. However, consider the following different set of hypotheses: Null hypothesis : The car ...
Invoking the mean ergodic theorem (discussed in this previous post), this assertion is in turn equivalent to the observable that corresponds to the Liouville function being orthogonal to the invariant factor of ; equivalently, the first Gowers-Host-Kra seminorm of (as defined for instance in ...
That’s common enough in 2018, but back in the day it was a real challenge, so the capabilities of the motor and electronics were compromised. The WM-D6C not only runs from four ‘AA’ cells, for a 6 volt supply, but does even better. Almost the first thing it does is step up th...
In the real world a vendor will wait for the transaction to be burried some levels deep in the blockchain before cashing out your purchase. By this I mean they will wait for the transaction to be part of a valid block on the chain and then wait longer until that block is followed by...
• You can’t hear the error in a signal truncated to 24 bits because it’s buried in the thermal noise of the 24-bit converters and subsequent electronics. That does still leave your contention that those signals can add up if we’re talking about summing many truncated 24-bit signals...
where and range over the zeroes and poles of respectively (counting multiplicity) in the disk . One can view (3) as a truncated (or localised) variant of (1). Note also that the summands are always non-positive. Proof: By perturbing slightly if necessary, we may assume that none ...
Indeed, if denotes the asymptotic mean in , then we have (heuristically at least) and we obtain the desired consistency after multiplying by . This still however does not explain the presence of the factor. Intuitively it is reasonable that if has many prime factors, and has a lot of ...