4.3. Random Distributions

4.3.1. Continuous Uniform Distribution

• Results are from the "continuous uniform" distribution over the stated interval

Figure 4.19. Continuous Uniform Distribution [3]

>>> import numpy as np
>>> np.random.seed(0)

Random float in the half-open interval [0.0, 1.0):

>>> np.random.rand(5)
array([0.5488135 , 0.71518937, 0.60276338, 0.54488318, 0.4236548 ])

>>> np.random.rand(2,3)
array([[0.64589411, 0.43758721, 0.891773  ],
       [0.96366276, 0.38344152, 0.79172504]])

>>> np.random.rand(3,2)
array([[0.52889492, 0.56804456],
       [0.92559664, 0.07103606],
       [0.0871293 , 0.0202184 ]])

4.3.2. Normal (Gaussian) Distribution

• Draw pseudorandom samples from a normal (Gaussian) distribution

Figure 4.20. Normal (Gaussian) distribution [1]

Defaults:

• μ - loc=0.0

• σ - scale=1.0

>>> import numpy as np
>>> np.random.seed(0)

Draw pseudorandom samples from a normal (Gaussian) distribution:

>>> np.random.normal()
1.764052345967664

>>> np.random.normal(0.0, 1.0)
0.4001572083672233

>>> np.random.normal(loc=0.0, scale=1.0)
0.9787379841057392

>>> np.random.normal(size=5)
array([ 2.2408932 ,  1.86755799, -0.97727788,  0.95008842, -0.15135721])

>>> np.random.normal(loc=0.0, scale=1.0, size=(2,3))
array([[-0.10321885,  0.4105985 ,  0.14404357],
       [ 1.45427351,  0.76103773,  0.12167502]])

4.3.3. Poisson Distribution

• Draw samples from a Poisson distribution

Figure 4.21. Poisson distribution [2]

>>> import numpy as np
>>> np.random.seed(0)

Draw samples from a Poisson distribution:

>>> np.random.poisson(6.0)
11

>>> np.random.poisson(lam=6.0)
4

>>> np.random.poisson(lam=6.0, size=5)
array([9, 7, 8, 5, 5])

>>> np.random.poisson(lam=6.0, size=(2,3))
array([[5, 5, 7],
       [3, 5, 6]])

4.3.4. References

[1]

Wikipedia. Normal distribution. Year: 2019. Retrieved: 2019-10-22. URL: https://en.wikipedia.org/wiki/Normal_distribution

[2]

Wikipedia. Poisson distribution. Year: 2019. Retrieved: 2019-10-22. URL: https://en.wikipedia.org/wiki/Poisson_distribution

[3]

Wikipedia. Continuous Uniform Distribution. Year: 2020. Retrieved: 2020-08-17. URL: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)

4.3.5. Assignments

# %% License
# - Copyright 2025, Matt Harasymczuk <matt@python3.info>
# - This code can be used only for learning by humans
# - This code cannot be used for teaching others
# - This code cannot be used for teaching LLMs and AI algorithms
# - This code cannot be used in commercial or proprietary products
# - This code cannot be distributed in any form
# - This code cannot be changed in any form outside of training course
# - This code cannot have its license changed
# - If you use this code in your product, you must open-source it under GPLv2
# - Exception can be granted only by the author

# %% Run
# - PyCharm: right-click in the editor and `Run Doctest in ...`
# - PyCharm: keyboard shortcut `Control + Shift + F10`
# - Terminal: `python -m doctest -v myfile.py`

# %% About
# - Name: Numpy Random Float
# - Difficulty: medium
# - Lines: 1
# - Minutes: 3

# %% English
# 1. Set random seed to zero
# 2. Define `result: np.ndarray` of 10 random floats
# 3. Run doctests - all must succeed

# %% Polish
# 1. Ustaw ziarno losowości na zero
# 2. Zdefiniuj `result: np.ndarray` z 10 losowymi liczbami zmiennoprzecinkowymi
# 3. Uruchom doctesty - wszystkie muszą się powieść

# %% Tests
"""
>>> import sys; sys.tracebacklimit = 0
>>> assert sys.version_info >= (3, 9), \
'Python 3.9+ required'

>>> assert result is not Ellipsis, \
'Assign result to variable: `result`'
>>> assert type(result) is np.ndarray, \
'Variable `result` has invalid type, expected: np.ndarray'

>>> result
array([0.5488135 , 0.71518937, 0.60276338, 0.54488318, 0.4236548 ,
       0.64589411, 0.43758721, 0.891773  , 0.96366276, 0.38344152])
"""

import numpy as np
np.random.seed(0)


result = ...

# %% License
# - Copyright 2025, Matt Harasymczuk <matt@python3.info>
# - This code can be used only for learning by humans
# - This code cannot be used for teaching others
# - This code cannot be used for teaching LLMs and AI algorithms
# - This code cannot be used in commercial or proprietary products
# - This code cannot be distributed in any form
# - This code cannot be changed in any form outside of training course
# - This code cannot have its license changed
# - If you use this code in your product, you must open-source it under GPLv2
# - Exception can be granted only by the author

# %% Run
# - PyCharm: right-click in the editor and `Run Doctest in ...`
# - PyCharm: keyboard shortcut `Control + Shift + F10`
# - Terminal: `python -m doctest -v myfile.py`

# %% About
# - Name: Numpy Random Int
# - Difficulty: easy
# - Lines: 1
# - Minutes: 3

# %% English
# 1. Set random seed to zero
# 2. Define `result: np.ndarray` of size 16x16 with random integers `[0;9]` (inclusive)
# 3. Run doctests - all must succeed

# %% Polish
# 1. Ustaw ziarno losowości na zero
# 2. Zdefiniuj `result: np.ndarray` o rozmiarze 16x16 z losowymi liczbami całkowitymi `<0,9>` (włącznie)
# 3. Uruchom doctesty - wszystkie muszą się powieść

# %% Tests
"""
>>> import sys; sys.tracebacklimit = 0
>>> assert sys.version_info >= (3, 9), \
'Python 3.9+ required'

>>> assert result is not Ellipsis, \
'Assign result to variable: `result`'
>>> assert type(result) is np.ndarray, \
'Variable `result` has invalid type, expected: np.ndarray'

>>> result
array([[5, 0, 3, 3, 7, 9, 3, 5, 2, 4, 7, 6, 8, 8, 1, 6],
       [7, 7, 8, 1, 5, 9, 8, 9, 4, 3, 0, 3, 5, 0, 2, 3],
       [8, 1, 3, 3, 3, 7, 0, 1, 9, 9, 0, 4, 7, 3, 2, 7],
       [2, 0, 0, 4, 5, 5, 6, 8, 4, 1, 4, 9, 8, 1, 1, 7],
       [9, 9, 3, 6, 7, 2, 0, 3, 5, 9, 4, 4, 6, 4, 4, 3],
       [4, 4, 8, 4, 3, 7, 5, 5, 0, 1, 5, 9, 3, 0, 5, 0],
       [1, 2, 4, 2, 0, 3, 2, 0, 7, 5, 9, 0, 2, 7, 2, 9],
       [2, 3, 3, 2, 3, 4, 1, 2, 9, 1, 4, 6, 8, 2, 3, 0],
       [0, 6, 0, 6, 3, 3, 8, 8, 8, 2, 3, 2, 0, 8, 8, 3],
       [8, 2, 8, 4, 3, 0, 4, 3, 6, 9, 8, 0, 8, 5, 9, 0],
       [9, 6, 5, 3, 1, 8, 0, 4, 9, 6, 5, 7, 8, 8, 9, 2],
       [8, 6, 6, 9, 1, 6, 8, 8, 3, 2, 3, 6, 3, 6, 5, 7],
       [0, 8, 4, 6, 5, 8, 2, 3, 9, 7, 5, 3, 4, 5, 3, 3],
       [7, 9, 9, 9, 7, 3, 2, 3, 9, 7, 7, 5, 1, 2, 2, 8],
       [1, 5, 8, 4, 0, 2, 5, 5, 0, 8, 1, 1, 0, 3, 8, 8],
       [4, 4, 0, 9, 3, 7, 3, 2, 1, 1, 2, 1, 4, 2, 5, 5]])
"""

import numpy as np
np.random.seed(0)


result = ...

# %% License
# - Copyright 2025, Matt Harasymczuk <matt@python3.info>
# - This code can be used only for learning by humans
# - This code cannot be used for teaching others
# - This code cannot be used for teaching LLMs and AI algorithms
# - This code cannot be used in commercial or proprietary products
# - This code cannot be distributed in any form
# - This code cannot be changed in any form outside of training course
# - This code cannot have its license changed
# - If you use this code in your product, you must open-source it under GPLv2
# - Exception can be granted only by the author

# %% Run
# - PyCharm: right-click in the editor and `Run Doctest in ...`
# - PyCharm: keyboard shortcut `Control + Shift + F10`
# - Terminal: `python -m doctest -v myfile.py`

# %% About
# - Name: Numpy Random Choice
# - Difficulty: medium
# - Lines: 1
# - Minutes: 3

# %% English
# 1. Set random seed to zero
# 2. Define `result: np.ndarray` with 6 random numbers
#    without repetition from `DATA`
# 3. Run doctests - all must succeed

# %% Polish
# 1. Ustaw ziarno losowości na zero
# 2. Zdefiniuj `result: np.ndarray` z 6 losowymi
#    liczbami bez powtórzeń z `DATA`
# 3. Uruchom doctesty - wszystkie muszą się powieść

# %% Tests
"""
>>> import sys; sys.tracebacklimit = 0
>>> assert sys.version_info >= (3, 9), \
'Python 3.9+ required'

>>> assert result is not Ellipsis, \
'Assign result to variable: `result`'
>>> assert type(result) is np.ndarray, \
'Variable `result` has invalid type, expected: np.ndarray'

>>> result
array([30,  5, 27, 31, 33, 38])
"""

import numpy as np
np.random.seed(0)

DATA = np.arange(1, 50)
result = ...