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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2017 • Question 9

Question

Math 6010 • Linear Models Fall 2017 • Question 9

Assume that the lifetimes of 100 lightbulbs are iid random variables with an Exponential(5) distribution, meaning that their common pdf is \[ f(x;\theta )=\frac {1}{5}e^{-x/5}, \qquad x>0. \] Use normal approximation to estimate the probability that in total the 100 lightbulbs last longer than 550 hours. You can express your answer as an integral.

Raw LaTeX

Assume that the lifetimes of 100 lightbulbs are iid random
variables with an Exponential(5) distribution, meaning that their common pdf is
\[
  f(x;\theta)=\frac{1}{5}e^{-x/5}, \qquad x>0.
\]
Use normal approximation to estimate the probability that in total the 100
lightbulbs last longer than 550 hours. You can express your answer as an
integral.

Topic Tags

Estimator Distributions Measure-Theoretic Probability Multivariate Normal Distributions Uniform Integrability and Truncation Methods