Distributions: interview questions and key results

Normal, Poisson, exponential, binomial. The results to know for quant trading interviews, then a worked example of each of the 5 question types. Free, no sign-up.

Practise endless questions like these

Key results

Standardise: z = (x − μ)/σ.
Poisson(λ): mean = var = λ.
Exponential(λ): mean 1/λ, memoryless.
Uniform(a,b): var (b−a)²/12.

Worked examples (5)

Try each one before opening the solution. In the app, every type generates fresh numbers each time.

Normal tails

X ~ N(μ = 135, σ = 20). Find P(X > 155).

Φ(0.5)=0.6915 · Φ(1)=0.8413 · Φ(1.5)=0.9332 · Φ(1.645)=0.95 · Φ(1.96)=0.975 · Φ(2)=0.9772 · Φ(2.5)=0.9938 · Φ(3)=0.9987

Answer and worked solution

Answer: 0.15866

Standardise: z = (155 − 135)/20 = 1. P(Z > 1) = 1 − Φ(1) ≈ 0.15866. Remember Φ(−z) = 1 − Φ(z).

Poisson probabilities

Orders arrive as a Poisson process averaging 6 per minute. What is the probability of exactly 1 orders in a given minute?

Answer and worked solution

Answer: 0.014873

P(N = 1) = e⁻⁶·6¹/1! ≈ 0.014873.

Exponential memorylessness

Waiting time T ~ Exponential(rate λ = 0.5). Given you've already waited 3, what is P(T > 6 | T > 3)?

Answer and worked solution

Answer: 0.22313

The exponential distribution is memoryless: P(T > s+t | T > s) = P(T > t) = e^−λt = e^−1.5 ≈ 0.22313. The 3 already waited is irrelevant.

Uniform variance

X ~ Uniform(-9, 8). What is Var(X)?

Answer and worked solution

Answer: 289/12 ≈ 24.083

Var = (b − a)²/12 = 289/12 ≈ 24.083.

Binomial "at most one"

A strategy makes 17 independent trades per week, each losing with probability 0.05. What is the probability of at most one losing trade in a week?

Answer and worked solution

Answer: 0.79223

Binomial(17, 0.05): P(X ≤ 1) = (1−p)¹⁷ + 17p(1−p)¹⁶ ≈ 0.41812 + 0.37411 = 0.79223.

Distributions: interview questions and key results

Key results

Worked examples (5)

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