891 B
891 B
Deterministic possibilities
All the different possible outcomes.
Random two bit number has deterministic possibilities 00, 01, 10, 11.
Probability distribution
A Probability for each possibility: Pr[x] = p where p \in [0,1]
For a coin flip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2
Combine all probabilities for all possible outcomes as vector to get probability distribution+
A valid distribution d has \sum d_i = 1 and for all i is d_i \geq 0
For a coin flip the probability distribution would be d_coin \in \mathbb{R}^2 with d = (1/2, 1/2)^t
Probabilistic processes
A probabilistic process is a Matrix A \in \mathbb{R}^{N \times N} if every column of A is a valid probability distribution.
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An example for generating a 2 bit number and then using a bit flip device to flip both
bits with a probability of 1/3