Calculate Particle Survival Probability After Time t
UpstartData Scientist · Technical Screen
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This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Calculate Particle Survival Probability After Time t states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.
Scenario
Radioactive-decay style process: 100 independent particles, each has a known half-life. Interviewer wants theoretical probability of how many survive after a given time.
Question
Given 100 identical particles with half-life H (each decays independently with exponential distribution), derive the probability that exactly k (or at least one) particles remain undecayed after time t.
Hints
Recall exponential survival function P(T>t)=e^{-λt} where λ=ln2/H; use Binomial distribution on independent survival events.
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