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Bernoulli Distribution (Discrete)

!uv pip install -q \
    pandas==2.3.3 \
    numpy==2.3.2 \
    scipy==1.16.2 \
    altair==5.5.0 \
    matplotlib==3.10.6 \
    sympy==1.14.0 \
    latexify-py==0.4.4

Models a single experiment with exactly two outcomes: Success (\(k=1\)) or Failure (\(k=0\)).

• Parameters: \(p\) (probability of success)
• Function: PMF
• Mean (\(E[X]\)): \(p\)
• Variance (\(\sigma^2\)): \(p \cdot q\) (where \(q = 1-p\))

Use Case & Example:

Scenario	Question	\(p\)	\(q\)
Coin Flip	Will the next flip be Heads (\(k=1\))?	\(0.5\)	\(0.5\)
Quality Control	Will the next item on the line be Defective (\(k=1\))?	\(0.02\)	\(0.98\)
Sales	Will the next website visitor make a Purchase (\(k=1\))?	\(0.1\)	\(0.9\)