Derive a CDF from a PDF
Company: Uber
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
During a first-round Data Scientist interview, you are asked a coding-and-statistics question:
You are given a valid probability density function `f(x)` for a continuous random variable `X`. Explain how to derive the cumulative distribution function `F(x)` from the PDF.
Your answer should cover:
- the mathematical definition of a CDF
- how to handle bounded or piecewise support
- boundary conditions such as `F(-infinity) = 0` and `F(infinity) = 1`
- how to verify that the result is a valid CDF
- how you would compute an approximate CDF in code if the PDF is available only numerically rather than in closed form
State any assumptions clearly.
Quick Answer: This question evaluates a candidate's understanding of the relationship between probability density functions and cumulative distribution functions, including handling bounded or piecewise support, boundary conditions like limits at ±infinity, verification of a valid CDF, and clarity in stating modeling assumptions.