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 ) = ex I { x > } . Let Z be standard normal and independent of X . Let T = X + Z . Given that T = 0 (exactly, or to 10 signiﬁcant digits, whichever you prefer), ﬁnd 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 ﬂy enters the room, the length of time that it stays is uniformly distributed between 0 minutes and 1 minute. Diﬀerent “sojourn times”are independent. What is the probability that there are exactly 2 ﬂies in the room at a given time? 1...
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 Spring '09
 Normal Distribution, Poisson Distribution, Probability theory, #, 0 minutes, Bulb, exponential lifetimes

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