A statistic for mean failure time has an exponential distribution with parameter lambda.
Recall the exponential distribution has density function f(t) = lambda * exp(-lambda * t) and cumulative distribution function F(t) = 1-exp(-lambda*t).
A group of interns have designed an experiment and will reject their null hypothesis that lambda = 0.5 if the statistic is greater than log(4). If the true lambda = 1 then what is the power of their experiment?