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Additional Practice Problems for Midterm 2 IOE 265, Fall 2010 1. The lifetime of 2 light bulbs for a particular lamp are independent random variables. Let X=lifetime of first bulb and Y=lifetime of the second bulb (both in 1000’s of hours). Suppose X and Y follow the exponential distribution with parameter λ=1 a. What is the joint pdf b. What is the probability that each bulb lasts at most 1000 hrs (i.e., X<1 and Y<1) c. What is the probability that the total lifetime of the 2 bulbs is at most 2? 2. For the following joint distribution a. Compute the covariance between X and Y if E(X)=E(Y)=25.329 and V(X)=V(Y)=8.2664 b. Compute the correlation b.

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3. The time taken in minutes to fill out a mortgage application for a random individual ~ N(10,4). If 5 individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time on each day is at most 11 min 4. Suppose you machine engine cylinders.
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