The life lengths of a certain population of batteries is wel

The life lengths of a certain population of batteries is well modeled by in exponential distribution having lambda = 0.004/hr. What is the probability that 200 hour old battery from this population will survive for an additional 300 hours?

Solution

Given X follows Exponential distribution with lamda=0.004 per hour

F(x)= 1-exp(-0.004*x) for x>0

So the probability is

P(X>300|X>200) = P(X>300) (because memoryless)

= 1-F(300)

=1-(1-exp(-0.004*300))

=0.3011942