Mathematics — Probability · continuous-density-functions
Problem
Assume that a new light bulb will burn out after t hours, where t is chosen from [0,∞) with an exponential density
f(t)=λe−λt.
In this context, λ is often called the failure rate of the bulb.
(a) Assume that λ=0.01, and find the probability that the bulb will not burn out before T hours. This probability is often called the reliability of the bulb.
(b) For what T is the reliability of the bulb =1/2?