The lifetime (in hours) of a lightbulb is an exponentially distributed random variable with parameter λ = 0.05
a) What is the probability that the light bulb is still burning three days after it is installed
b) Assume that the bulb was installed at noon today and assume that at 5:00 pm today you notice that the bulb is still working.
i) What is the chance that the bulb will burn out at some time between 4:30 pm and 6:00 pm today
ii) What is the expected time when the bulb burns out? (again, given that it was still working at 5:00 pm today)