Calculate Expected Draws for X > 0.8 in Uniform(0,1)

Q: Calculate Expected Draws for X > 0.8 in Uniform(0,1)

This question evaluates a candidate's understanding of basic probability concepts and expected value in the context of random sampling. It is commonly asked to gauge statistical intuition about sampling and rare-event frequency, falls under the Statistics & Math category, and tests conceptual understanding rather than practical implementation.

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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

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Scenario

Quick probability check during a first-round screen to gauge statistical intuition.

Question

Let X ~ Uniform(0, 1). You draw independent samples X1, X2, … from this distribution.

On average, how many draws are needed until you first observe a value greater than 0.8?

Assumption: Each draw is independent and identically distributed (i.i.d.).
Hint: Model the number of trials with a geometric distribution.

Calculate Expected Draws for X > 0.8 in Uniform(0,1)

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Calculate Expected Draws for X > 0.8 in Uniform(0,1)

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