hw3soln

hw3soln - Problem 1 Wile E Coyote loves his ACME...

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Problem 1 Wile E. Coyote loves his ACME Corporation gadgets. The ACME Co. dynamite sticks Mr. Coyote recently purchased included a timed fuse that was rated for 10 seconds of burn. Unbeknownst to Mr. Coyote, the fuse burn time follows a normal distribution with a mean of 10 seconds and a standard deviation of 5 seconds. a. Wile E. Coyote has allowed 4.5 seconds for his escape after lighting the fuse. What is the probability that things will end badly on account of the fuse burn time? b. Mr. Coyote sneaks away from the lit fuse at 1 m/s. What is the mean distance he will reach before the dynamite explodes? c. Following complaints about their low grade fuses, ACME co. switches to a different fuse style with a uniform distribution between 3 and 8 seconds of burn time. Will this improve Wile E. Coyote’s escape probability or mean distance reached? a. From the Gaussian distribution ݐ ̅ ൌ 10, ߪ ൌ5 ܲሾܾܽ݀ ݐ݄݅݊݃ݏሿൌܲሾݐ൏4 .5ሿ ݖ ଵ଴ିସ.ହ ൌ1 .1 ܲሾݐ൏4 .5ሿ ൌ ܲൣݖ ൧ൌ ∙ 0.7287 ൌ 0.1357 b. Using expected value of the calculated quantity, ܧሾݔሿൌܧሾݒ∙ݐሿൌݒ∙ܧሾݐሿൌ1 ∙ 10ݏ ߤ ൌ 10 ݉ c. For the uniform distribution, .5ሿ ൌ ׬ ݌ሺݐሻ݀ݐ ସ.ହ ିஶ ൌ ׬ ݀ݐ ସ.ହ ሺ4.5 െ 3ሻ ൌ 0.3000 No, this does not improve his escape probability.
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This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue.

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hw3soln - Problem 1 Wile E Coyote loves his ACME...

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