320_hw7_ans - Economics 320: Homework 7 Continuous...

320_hw7_ans
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Economics 320: Homework 7 Continuous Distributions: Exponential Sampling Distributions EXPONENTIAL DISTRIBUTION: 1. Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.1 claims per month. a. What is the probability that the dealership will wait at least 6 months until the next claim? i. λ is the mean number of occurrences per time unit ; so λ = 0.1 ii. F(x) = 1 - x e λ - for x > 0. iii. P(x > 6) = x e - = 6 * 1 . 0 - e = 0.5488 b. At least a year? i. P(x > 12) = x e - = 12 * 1 . 0 - e = 0.3012 c. At least 6 months but not more than 1 year? i. P(6 < x < 12) = (1 - 12 * 1 . 0 - e ) - (1 - 6 * 1 . 0 - e ) = 0.2476 2. In 1982, the in-flight shutdown rate for the Garrett TFE731 turbofan engine was 6.0 shutdowns per 100,000 hours. In 1992, with improvements, the in-flight shutdown rate for this same engine dropped to 1.5 shutdowns per 100,000 hours. a. Find the probability that at least 50,000 hours would elapse before the next in- flight shutdown in 1982. i. λ is the mean number of occurrences per time unit ; so λ(1982) = 6 and λ(1992) = 1.5 ii. for 1982: P(x > ½) = 5 . 0 * 6 - e = 0.0498 b. Calculate the same probability in 1992. i.
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