A natural logarithmic base is not required for which of these distributions for probability calculations?

The correct answer is B. Binomial. Binomial is the only distribution among these whose probability formula relies solely on combinations and powers - P(X = k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ - with no appearance of e anywhere. The Poisson PMF explicitly contains e⁻λ (e.g., P(X=k) = λᵏe⁻λ/k!), making e unavoidable. The…

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Options

AWeibull
BBinomial
CPoisson
DNormal

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(32 responses)

A
16% (5)
B
72% (23)
C
3% (1)
D
9% (3)

Explanation

Binomial is the only distribution among these whose probability formula relies solely on combinations and powers - P(X = k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ - with no appearance of e anywhere. The Poisson PMF explicitly contains e⁻λ (e.g., P(X=k) = λᵏe⁻λ/k!), making e unavoidable. The Normal PDF has e raised to the squared z-score in its exponent, and the Weibull PDF also carries an e^(−(x/λ)ᵏ) term, so both require e as well.

Memory tip: Think "Binomial = Bernoulli trials = coin flips = just counting successes." Counting problems use factorials and powers, not exponential growth - that's why e never shows up.

Topics

#Probability Distributions#Statistical Analysis#Natural Logarithm#Distribution Theory

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