course Mth 174 DόQʃassignment #011
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10:29:17 Query 8.8.2 (3d edition 8.7.2) 8.7.2. Probability and More On Distributions, p. 421 daily catch density function piecewise linear (2,.08) to (6.,24) to (8,.12)
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RESPONSE --> The problem is to find the mean daily catch here. To do that, I use the integral of the density function multiplied by the variable, like: int( xp(x) ) In this function, there are two parts to the formula, from 2 to 6 and from 6 to 8. The rates are given below: p(x) = 0.04x for 2 <= x <=6 p(x) = -0.06x - 0.6 for 6 <= x <= 8 To find the mean of these two functions, I just need to integrate them according to the formula above and add them together: int (x*0.04x, x, 2, 6) = 2.773 int (x*(-0.06x - 0.6), x, 6, 8) = 2.48 Overall mean = 2.773 + 2.48 = 5.2533
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10:29:39 what is the mean daily catch?
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RESPONSE --> 5.2533 tons of fish.
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10:30:32 What integral(s) did you perform to compute a mean daily catch?
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RESPONSE --> int (x*0.04x, x, 2, 6) and int (x*(-0.06x - 0.6), x, 6, 8)
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10:31:04 What does this integral have to do with the moment integrals calculated in Section 8.3?
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RESPONSE --> The formula is the same and so is the idea: to find the balance point of the graph.
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10:32:55 Query 8.8.13 (3d edition 8.7.13). Probability and More On Distributions, p. 423 cos t, 0
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RESPONSE --> Ok.
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10:34:40 which function might best represent the probability for the time the next customer walks in?
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RESPONSE --> (b) p(t) = 3e^(-3t)
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12:11:45 for each of the given functions, explain why it is either appropriate or inappropriate to the situation?
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RESPONSE --> (a) p(x) = cos t for 0<= t <= 2'pi and e^(t-2'pi) for t>= 2'pi. This is unacceptable because cos t becomes negative for part of 0 to 2'pi and a probability density function can never be less than 0. (b) p(x) = 3e^(-3t) This works because it is positive for all values of x and the integral from 0 to infinity is 1. So this is the most likely to be a probability density function. (c) p(x) = e^(-3t) for t >=0 Values are positive for all values of x since 0 is the asymptote for this function, but the integral does not approach 1, staying rather at 1/3. Since a probability density function must equal 1 for the period, this isn't an acceptable function. (d) p(x) = 1/4 for 0 <= t <= 4 First off, is the store open only 4 minutes? Besides which, the integral diverges and never approaches 1, so it can't be a probability density function.
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12:12:07 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> More applications of the same basic functions to different types of needs. Very interesting.
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