Probability that the detector lasts longer than 2 years > There is a detector in a satellite orbiting the earth. The lifetime (in years) of the detector is a random number $X$, that has exponential distribution with parameter 1/2. What is the probability that the detector lasts longer than 2 years? **Solution attempt:** $${\text{P}}({\text{detector lasts longer than 2 years)}} = 1 - {\text{P(detector lasts no more than 2 years)}}$$ $${\text{P}}({\text{detector lasts longer than 2 years)}} = 1 - 0.5 \cdot \sum\limits_{k = 0}^2 {{e^{ - 0.5x}}} \approx 0.01279$$ Is my solution correct?

No, the cumulative distribution function of an exponentially distributed random variable is $$F_X(x) = \Pr[X \le x] = 1 - e^{-\lambda x},$$ where $\lambda$ is a rate parameter. So, the probability that the lifetime exceeds $2$ is $$\Pr[X > 2] = e^{-2\lambda}.$$ The problem is that when the question says "$X$ has exponential distribution with parameter $1/2$," it is not clear whether they mean that this parameter is a rate parameter, or a scale parameter; i.e., do they mean $\lambda = 1/2$, or $1/\lambda = 1/2$? This is ambiguous.