Calculate probability with given parameter

Question provides the complete PDF or CDF with a specific numerical parameter value and asks to calculate probabilities or percentiles directly.

2 questions

CAIE FP2 2019 June Q6
6 The random variable \(T\) is the lifetime, in hours, of a randomly chosen battery of a particular type. It is given that \(T\) has a negative exponential distribution with mean 400 hours.
  1. Write down the probability density function of \(T\).
  2. Find the probability that a battery of this type has a lifetime that is less than 500 hours.
  3. Find the median of the distribution.
CAIE FP2 2018 November Q7
7 The random variable \(T\) is the lifetime, in hours, of a particular type of battery. It is given that \(T\) has a negative exponential distribution with mean 500 hours.
  1. Write down the probability density function of \(T\).
  2. Find the probability that a randomly chosen battery of this type has a lifetime of more than 750 hours.
  3. Find the median value of \(T\).