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A manufacturer has deaigned a process to produce pipes that ara 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 faat to 10.57 fest. Assume that the langtha of individual pipe the procoss are indapendent. Lot X and Y raprasent the langths of two different pipes produced by tha process. produced by a) What is the joint pdf for X and Y f(x,y)-1/(0.57)2 f(x,y) Kx,y)-1/(0.57)2 10 ? 10 ? ? 11, 10 ? y ? 11 O 1 10 10.57, 10 ? y 10.57 ? 10.57, 10 ? y ? 10.57 Oflx,y)=xy 10? x 10.57, 10 yS 10.57 b) what is the probability that a single pipe will be between 10.18 feet and 10.4 feet long? Give your·nswer to four decimal places. c) What is the probability that both pieces of pipe are between 10.18 feet and 10.4 feet long? Give your answer to four decimal places. Hint: Try to avoid doing calculus to solve this problem. ) Whet is the expected length of a single pipe? Give your answer to threeplaces e) What is the expected total length of the two pieces of pipe? Give your answer to three decimal places. f) What is the variance of the length of a single pipe? Give your answer to four decimal places. ) What is the variance of the total length of both pipes? Give your answer to four decimal places. h)What is the probability that the second pipe (with length Y) is more than 0.22 feet longer than the first pipe (with length X)? Give your answer to four decimal places. Hint: Do not use calculus to get your answer

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