What the Nyquist theorem says: sample at ≥ 2× the highest frequency to avoid aliasing

What CAP theorem states: you can have at most 2 of consistency, availability, partition tolerance

CAP theorem: Consistency, Availability, Partition Tolerance; only 2 can be fully achieved simultaneously

What rejection sampling does: samples from target by accepting/rejecting proposals

Rejection sampling generates samples from a target distribution by accepting or rejecting proposals based on a comparison with a uniform distribution

What Chebyshev's inequality says: P(|X-μ| ≥ kσ) ≤ 1/k²

Chebyshev's inequality states that the probability of a random variable deviating from its mean by at least k standard deviations is less than or equal to 1/k²

What does the Shannon-Hartley theorem convey about the maximum data rate for a noisy channel in communication systems?

It states the channel capacity in bits per second, given bandwidth and signal-to-noise ratio

Shannon's channel capacity: C = B log₂(1 + S/N) bits per second

Shannon's formula: C = B log₂(1 + S/N) defines channel capacity in bits/s

What importance sampling does: reweights samples from proposal to estimate target expectation

Importance sampling reweights samples from a proposal distribution to approximate the expectation of a target distribution