Q5. (15 points) The lifetime (in hours) of a lightbulb is an exponentially distributed random variable with parameter \ 0.10 (units of hours-1). = (a) (5 points) What is the probability that the light bulb is still burning one day (24 hours) after it is installed? (b) Assume that the bulb was installed at noon today and assume that at 3:00pm today you notice that the bulb is still working. You stick around until 3:30pm, and the bulb is still working when you leave. (b-i) (5 points) What is the chance that the bulb will burn out at some time between 4:30pm and 6:00pm today? (b-ii) (5 points) What is the expected time when the bulb burns out? (again, given that it was still working at 3:30pm today)