has a hole. Your task is to determine the location of this Graph 2: The graph of
ID: 2879903 • Letter: H
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has a hole. Your task is to determine the location of this Graph 2: The graph of g(x) x-2, hole using approximation techniques (no fancy limit computations allo Lab P that reparation should be drawn at a scale a. Draw a graph of g using an entire sheet of paper. Your graph y scales should be chosen so gives a good sense o the xy coordinates of the hole. The x and that your graph nearly extends between two diagonally opposites corners of the page. Identify what unknown numerical value you will need to approximate. Give it an b. appropriate shorthand name (that is, a variable). c. Describe what you will use for approximations. description of your answer using algebraic notation (for example, function notation, variables, formulas, etc.) Lab: Work with your group on the problem assigned to you. We encourage you to collaborate individually. both in and out of class, but you must write up your responses approximation 1. Find an approximation to the height of the hole in your function (write out the how you with several decimal places). Is this underestimate or overestimate? Explain an know. Find both an underestimate and an overestimate. 2. your graph at a good scale to clearly illustrate how you can approximate the height of the hole. Label the unknown height and the approximation 3. Illustrate the error for your two approximations on your graph. Explain why you can't determine the numerical values of these errors. What is an algebraic representation for the error in your approximations? 4. Use your underestimate and overestimate to find a bound on the error for these two approximations. Explain your work. Illustrate this error bound on your graph 5. List three fairly decent pairs of underestimates and overestimates (you can include the one you computed above). For each pair, bound for the error and use this to determine a range of possible values for the actual y value of the hole in a table with headers as shown. Range of Possible Values Error Bound Underestimate Then describe as best as 6. Find an approximation with error smaller than you can all of the x-values you could use to get approximations that would have an error smaller than this error bound you find an approximation with error smaller than that bound? Explain in detail how you know, O CLEAR Calculus 2010Explanation / Answer
5) We consider three approximate-likelihood approaches to estimating a constant recombination rate, , from sequence variation data from a region of interest. These are two composite-likelihood approaches and an approach based on using the likelihood for a simplified model.
To calculate each team's strength of schedule we need to know quantify the strength of each of their opponents. This can be done using statistical methods based on the results of matches within the current season. However this only gives us an estimate of the strength of each team, and there is corresponding uncertainty in these estimates. (This uncertainty is particularly large towards the beginning of the season.) The margin of error quantifies the corresponding uncertainty in the estimates of the strength of schedule. We define the margin of error so that the chance of the SOS being wrong by more than the margin of error in a particular direction is about 5%.
Consider Creighton in 2008/09. Their strength of schedule is estimated as 26.5, but the margin of error is 0.6. Thus their actual strength of schedule could lie anywhere from 27.1 to 25.9 (i.e. 26.5 plus or minus 0.6), though it is most likely to 26.5.
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