141 141141 1412010-04-09 17:33:32 / rev 6d18933f3e28+7Lumping7.1 Estimating populations: How many babies? 1337.2 Bending of light 1357.3 Quantum mechanics 1387.4 Sound and electromagnetic radiation 1437.5 Boundary layers 143The symmetry chapter (Section 3.1) introduced the principle of invariance:‘When there is change, look for what does not change.’ However, whenyou cannot find any useful but unchanging quantity, you have to makeone. As Jean-Luc Picard often says, ‘Make it so.’7.1 Estimating populations: How many babies?The first example is to estimate the number of babies in the United States.For definiteness, call a child a baby until he or she turns 2 years old. Anexact calculation requires the birth dates of every person in the UnitedStates. This, or closely similar, information is collected once every decadeby the US Census Bureau.age(yr)106yr0 5004N(t)As an approximation to this voluminousdata, the Census Bureau [33] publishesthe number of people at each age. Thedata for 1991 is a set of points lying on awiggly line N(t), where t is age. ThenNbabies=Z2 yr0N(t) dt. (7.1)141 141141 1412010-04-09 17:33:32 / rev 6d18933f3e28+7Lumping7.1 Estimating populations: How many babies? 1337.2 Bending of light 1357.3 Quantum mechanics 1387.4 Sound and electromagnetic radiation 1437.5 Boundary layers 143The symmetry chapter (Section 3.1) introduced the principle of invariance:‘When there is change, look for what does not change.’ However, whenyou cannot find any useful but unchanging quantity, you have to makeone. As Jean-Luc Picard often says, ‘Make it so.’7.1 Estimating populations: How many babies?The first example is to estimate the number of babies in the United States.For definiteness, call a child a baby until he or she turns 2 years old. Anexact calculation requires the birth dates of every person in the UnitedStates. This, or closely similar, information is collected once every decadeby the US Census Bureau.age(yr)106yr0 5004N(t)As an approximation to this voluminousdata, the Census Bureau [33] publishesthe number of people at each age. Thedata for 1991 is a set of points lying on awiggly line N(t), where t is age. ThenNbabies=Z2 yr0N(t) dt. (7.1)Global comments 1Global commentsI like how this section starts with a very easy example and then goes to a more complicatedone and then gives a more difficult practice problem.141 141141 1412010-04-09 17:33:32 / rev 6d18933f3e28+7Lumping7.1 Estimating populations: How many babies? 1337.2 Bending of light 1357.3 Quantum mechanics 1387.4 Sound and electromagnetic radiation 1437.5 Boundary layers 143The symmetry chapter (Section 3.1) introduced the principle of invariance:‘When there is change, look for what does not change.’ However, whenyou cannot find any useful but unchanging quantity, you have to makeone. As Jean-Luc Picard often says, ‘Make it so.’7.1 Estimating populations: How many babies?The first example is to estimate the number of babies in the United States.For definiteness, call a child a baby until he or she turns 2 years old. Anexact calculation requires the birth dates of every person in the UnitedStates. This, or closely similar, information is collected once every decadeby the US Census Bureau.age(yr)106yr0 5004N(t)As an approximation to this voluminousdata, the Census Bureau [33] publishesthe number of people at each age. Thedata for 1991 is a set of points lying on awiggly line N(t), where t is age. ThenNbabies=Z2 yr0N(t) dt. (7.1)141 141141 1412010-04-09 17:33:32 / rev 6d18933f3e28+7Lumping7.1 Estimating populations: How many babies? 1337.2 Bending of light 1357.3 Quantum mechanics 1387.4 Sound and electromagnetic radiation 1437.5 Boundary layers 143The symmetry chapter (Section 3.1) introduced the principle of invariance:‘When there is change, look for what does not change.’ However, whenyou cannot find any useful but unchanging quantity, you have to makeone. As Jean-Luc Picard often says, ‘Make it so.’7.1 Estimating populations: How many babies?The first example is to estimate the number of babies in the United States.For definiteness, call a child a baby until he or she turns 2 years old. Anexact calculation requires the birth dates of every person in the UnitedStates. This, or closely similar, information is collected once every decadeby the US Census Bureau.age(yr)106yr0 5004N(t)As an approximation to this voluminousdata, the Census Bureau [33] publishesthe number of people at each age. Thedata for 1991 is a set of points lying on awiggly line N(t), where t is age. ThenNbabies=Z2 yr0N(t) dt. (7.1)Comments on page 1 2Comments on page 1great file namethis seems like it should go with divide and conquer at the beginning of the semesterRead Sections 7.1 and 7.2 for Sunday’s memo. The final (fifth) page has a fun problemto think about, which we’ll look at on Monday. Have a nice weekend.I am still not convinced or do I understand the whole concept of lumping?I just got deja vu here...wasn’t this line used in a previous reading?I think so... and he’s used it in class a few times.Yah...he uses it a LOT in class. Sometimes its use is rather confusing, but it makessense here.Might as well call it, "As Sanjoy Mahajan says..."Yeah this has been used a ton of times it’s kind of a theme of the classThis seems like a very unspecific question and thus requires more difficulty in approxi-mating...it would help to ask maybe how many babies are born in __ time, or how manypeople between 0-2 are in the US?Um, I think you’re reading too much into this. This is just the title, and a little subtitleto go alongside the main topic of estimating populations. The actual question will beaddressed in the text.That’s the very first step that’s taken in the paragraph: defining the parameters of theproblem for estimation.I’ve been asked this exact question as part of consulting case interviews before, I reallylike seeing examples like this because they are so applicable to what I want to do in thefuture!True, but wasn’t this method a little too simple and also very sensitive to the guess youmade based on everyone dying at 75 years?I’d say that the method is not at all too simple...esp. for a problem you encounter ininterview where you need to thing quickly. Having a simple (but accurate) methodis extremely valuable.141 141141 1412010-04-09 17:33:32 / rev 6d18933f3e28+7Lumping7.1 Estimating populations: How many babies? 1337.2 Bending of light 1357.3 Quantum mechanics 1387.4 Sound and