Problems

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Bernoulli Probability Mass Function & Moments

Probability and Statistics

Easy

Implement the Bernoulli Probability Mass Function (PMF) and compute the distribution's mean and variance for given inputs.

Bernoulli Distribution:

Probability Mass Function:

P(X = 1) = p,\qquad P(X = 0) = 1 - p

Mean and Variance:

\mu = p,\qquad \sigma^2 = p(1 - p)

Function Arguments

x: scalar, list, or array - Values of 0s and 1s
p: float - Success probability (0 ≤ p ≤ 1)

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Examples

Input: x=[0, 1, 1], p=0.3

Output: pmf=[0.7, 0.3, 0.3], mean=0.3, var=0.21

Input: x=[1], p=0.8

Output: pmf=[0.8], mean=0.8, var=0.16

Input: x=[0, 1, 0, 1], p=0.5

Output: pmf=[0.5, 0.5, 0.5, 0.5], mean=0.5, var=0.25

Hint 1

Use np.where() to assign probabilities.

Hint 2

Mean is simply p, variance is p * (1 - p).

Hint 3

Convert to float using float() for mean and variance return values.

Requirements

Return tuple: (pmf, mean, var)
pmf: NumPy array of probabilities
mean, var: scalar floats
Vectorized implementation (no loops)
Convert x to NumPy array

Constraints

len(x) ≤ 1e6
0 ≤ p ≤ 1
NumPy only; time limit: 200ms

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