Problem 44315. Predicting life and death of a memory-less light bulb

💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡 💡

You have a light bulb that can fail any moment according to the exponential probability distribution.

At any moment, the probability that it will survive just N hours = exp(-N*P), where P is a constant.

Notice that this probability is very small if N is very large.

Now suppose, the bulb has already survived N hours.

Please calculate the probability of its surviving M more hours.

Solve

Last Solution submitted on Feb 10, 2020

cody5 decay expectation memory-less probability random stochastic