Grinstead-Snell-Probability · Problem 6.3.3

Sums of Random Variables

Mathematics · expected-value-variance-continuous

Problem

The lifetime, measured in hours, of the ACME super light bulb is a random variable

T

with density function

f_T(t) = \lambda^2 t e^{-\lambda t}

, where

\lambda = .05

. What is the expected lifetime of this light bulb? What is its variance?