16 lines
891 B
Markdown
16 lines
891 B
Markdown
### Deterministic possibilities
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All the different possible outcomes.
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`Random two bit number has deterministic possibilities 00, 01, 10, 11.`
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### Probability distribution
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A Probability for each possibility: Pr[x] = p where p $\in$ [0,1]
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`For a coin flip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2`
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Combine all probabilities for all possible outcomes as vector to get probability distribution+
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A valid distribution d has $\sum d_i = 1$ and for all i is $d_i \geq 0$
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For a coin flip the probability distribution would be $d_coin \in \mathbb{R}^2$ with $d = (1/2, 1/2)^t$
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### Probabilistic processes
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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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![[Pasted image 20260728163713.png]]
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An example for generating a 2 bit number and then using a bit flip device to flip both
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bits with a probability of 1/3 |