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**Unformatted text preview: **In the future, bulb #n will be immediately replaced upon burnout with bulb #(n+1). Calculate the probability that the bulb occupying the socket exactly 10 years from now is bulb #18. 4. Let X be a unit exponential random variable, with density f ( x ) = e-x I { x > } . Let Z be standard normal and independent of X . Let T = X + Z . Given that T = 0 (exactly, or to 10 signicant digits, whichever you prefer), nd the approximate numerical conditional probability that X > 2. 5. Flies enter a room according to a Poisson process with rate 3 per minute. Each time a y enters the room, the length of time that it stays is uniformly distributed between 0 minutes and 1 minute. Dierent sojourn timesare independent. What is the probability that there are exactly 2 ies in the room at a given time? 1...

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