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Sampling an exponential from a uniform

MediumRandom VariablesProgramming & DSA~4m

Given a uniform [0,1][0,1] variable UU, which transformation produces an Exp(λ)\text{Exp}(\lambda) sample?

Show hints (2)+
  1. Invert the CDF F(x) = 1 − e^(−λx).
  2. −ln U is exponential with rate 1.

Answer

Reveal answer →

X=−ln⁡UλX = -\dfrac{\ln U}{\lambda}

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