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S )"a� Random variable generators.
bytes
-----
uniform bytes (values between 0 and 255)
integers
--------
uniform within range
sequences
---------
pick random element
pick random sample
pick weighted random sample
generate random permutation
distributions on the real line:
------------------------------
uniform
triangular
normal (Gaussian)
lognormal
negative exponential
gamma
beta
pareto
Weibull
distributions on the circle (angles 0 to 2pi)
---------------------------------------------
circular uniform
von Mises
General notes on the underlying Mersenne Twister core generator:
* The period is 2**19937-1.
* It is one of the most extensively tested generators in existence.
* The random() method is implemented in C, executes in a single Python step,
and is, therefore, threadsafe.
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Used to instantiate instances of Random to get generators that don't
share state.
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generator of your own devising: in that case, override the following
methods: random(), seed(), getstate(), and setstate().
Optionally, implement a getrandbits() method so that randrange()
can cover arbitrarily large ranges.
� Nc C s | � |� d| _dS )zeInitialize an instance.
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a\ Initialize internal state from a seed.
The only supported seed types are None, int, float,
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system specific randomness source if available.
If *a* is an int, all bits are used.
For version 2 (the default), all of the bits are used if *a* is a str,
bytes, or bytearray. For version 1 (provided for reproducing random
sequences from older versions of Python), the algorithm for str and
bytes generates a narrower range of seeds.
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__reduce__� s zRandom.__reduce__c K sJ | j D ]>}d|jv r qFd|jv r.| j| _ qFd|jv r| j| _ qFqdS )a Control how subclasses generate random integers.
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into grand prize and second place winners (the subslices).
Members of the population need not be hashable or unique. If the
population contains repeats, then each occurrence is a possible
selection in the sample.
Repeated elements can be specified one at a time or with the optional
counts parameter. For example:
sample(['red', 'blue'], counts=[4, 2], k=5)
is equivalent to:
sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5)
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for sampling from a large population:
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positive infinity if lambd is positive, and from negative
infinity to 0 if lambd is negative.
r1 )r� r$ )r7 Zlambdr9 r9 r: r \ s zRandom.expovariatec C s� | j }|dkrt|� S d| }|td|| � }|� }tt| �}||| }|� } | d|| k s�| d| t|� kr4q�q4d| }
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Conditions on the parameters are alpha > 0 and beta > 0.
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x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) = --------------------------------------
math.gamma(alpha) * beta ** alpha
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