Problem 5 Two light bulbs have random duration lifetimes represented by random variables X and Y, both exponentially distributed with parameter A. Bulbs are used to light a workspace. Random variable Z represents the length of time that the workspace is sufficiently lit. Find the pdffz(z) if a) Light from both bulbs is needed in the workspace. b) Light from one bulb is sufficient, so the second bulb is used only if the first one fails. c) Light from one bulb is sufficient, but both bulbs are turned on and kept until both are dead