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This probably sounds weird, but are there any Wikipedia articles on the topic of "reconstructing" the function used in a table of values? For example, if I had a table:
x | 8 | 10 | 12 |
---|---|---|---|
y | 71 | 97 | 123 |
Just in case you didn't know, it means that f(8)=71, f(10)=97, and f(12)=123. I'm trying to find out what the function (f) is. I can then use a certain method to find that the function is . Is there any more information out there on this topic (the "reconstruction")?
-- wj32 t/ c 02:12, 18 January 2008 (UTC)
And solve for a, b, and c. Then (obviously) I put those values back into to get the original function. If I generalize the process a bit I can get formulas for a, b, and c:
In these formulas n means the "start" of the data. If I was solving the previous example n would be 8. z means the step between each input of the function. So in that case z would be 2. Obviously, we know f(n) (aka f(8)), f(n+z) (aka f(10)), and f(n+2z) (aka f(12)). So, we can work out the values of a, b, and c.
I'm a bit of a newb beyond the basic math we learn at school. So, now I've got three questions:
-- wj32 t/ c 03:05, 18 January 2008 (UTC)
You might find System of linear equations more helpful. With the three equations you get from three data points, you can solve to find the three coefficients of your polynomial, as you have done. Interpolation is sort of related, but I think you more want to know how to find the polynomial itself. Yes, this sort of thing is very well researched and applies to polynomials of any degree, and all sorts of other problems. As the number of equations get large, we have more "automated" ways of solving a system of equations, such as Gaussian elimination. - Rainwarrior ( talk) 05:33, 18 January 2008 (UTC)
first of al this isnt my homework question..!! so plz help me solve this question of fuji film.. it is for my own personal understanding....!! plz try and help me answer all questions..i have been trying to solve it since 3 days but aint gettin newhere m typing down the whole case here..
In the early 1990s, Fuji Photo Film, USA, joined forces with four of its rivals to create the Advanced Photo System (APS), which is hailed as the first major development in the film industry since 35 - millimeter technology was introduced. In February 1996, the new 24 millimeter system, promising clearer and sharper pictures, was launched. By the end of the year, the lack of communications and a limited supply of products made retailers angry and consumers baffled. Advertising was almost nonexistent. Because the product was developed by five industry rivals, the companies had enacted a secrecy agreement in which no one outside of company management, including the company's sales force, would know details about the product until each company introduced its APS products on the same day. When the product was actually introduced, it came with little communication to retailers about the product, virtually no training of sales representatives on the product ( so that they could demonstrate and explain the features ), and a great underestimation of demand for the product. Fortunately, Fuji pressed on by taking an "honesty is the best policy" stance and explaining to retailers and other costumers what had happened and asking for patience. In addition, Fuji increased its research to better ascertain market positioning and size. By 1997, Fuji had geared up production to meet the demand and was increasing customer promotion. APS products were on the road for success. By 1998, APS cameras owned 20% of the point and shoot camera market.
1. As stated, by 1998 APS cameras owned 20% of the point and shoot camera market. Now it is the year 2003 and the market share might be nearer to 40%. Suppose 30 cusomers from the point and shoot camera market are randomly selected. If the market share is really .40 , what is the expected number of point and shoot camera customers who purchase an APS camera? What is the probability that six or fewer purchases and APS camera? Suppose you actually got six or fewer APS customers in the sample of 30. Based on the probability just calculated, is this enogh evidence to convince you that the market share is 40% Why or why not?
2. Suppose customer complaints on the 24 millimeter film are poison distributed at an avegare rate of 2.4 complaints/100,000 rols sold. Suppose further that Fuji is having trouble with shipments being late and one batch of 100,000 rolls yields seven complaints from customers. Assuming that it is unacceptable to management for the average rate of complaints to increase, is this enough evidence to convince management that the average rate of complaints has increased, or can it be written off as a random occurence that happens quite frequently? Produce the Poisson distribution for this question and discuss its inplication for this problem.
3. One study of 52 product launches found that those undertaken with revenue growth as tha main objective are more likely to fail than those undertaken to increase customer satisfaction or to create a new market such as the APS system. Suppose of the 52 products launched, 34 were launched with revenue growth as the main objective and the rest were launched to increase cusotmer satisfaction or to create a new market. Now suppose only 10 of these products were successful ( the rest failed) and seven were products that were launched to increase customer satisfaction or to create a new market. What is the probability of this result occuring by chance? What does this probability tell you about the basic premise regarding the importance of the main objective? —Preceding unsigned comment added by 220.225.79.210 ( talk) 14:00, 18 January 2008 (UTC)
I need to know how many gigabytes is 153.44 megabytes and any many gigabytes is 4812 kilobytes? Thanks!
71.145.168.69 ( talk) 17:24, 18 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 17 | << Dec | January | Feb >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
This probably sounds weird, but are there any Wikipedia articles on the topic of "reconstructing" the function used in a table of values? For example, if I had a table:
x | 8 | 10 | 12 |
---|---|---|---|
y | 71 | 97 | 123 |
Just in case you didn't know, it means that f(8)=71, f(10)=97, and f(12)=123. I'm trying to find out what the function (f) is. I can then use a certain method to find that the function is . Is there any more information out there on this topic (the "reconstruction")?
-- wj32 t/ c 02:12, 18 January 2008 (UTC)
And solve for a, b, and c. Then (obviously) I put those values back into to get the original function. If I generalize the process a bit I can get formulas for a, b, and c:
In these formulas n means the "start" of the data. If I was solving the previous example n would be 8. z means the step between each input of the function. So in that case z would be 2. Obviously, we know f(n) (aka f(8)), f(n+z) (aka f(10)), and f(n+2z) (aka f(12)). So, we can work out the values of a, b, and c.
I'm a bit of a newb beyond the basic math we learn at school. So, now I've got three questions:
-- wj32 t/ c 03:05, 18 January 2008 (UTC)
You might find System of linear equations more helpful. With the three equations you get from three data points, you can solve to find the three coefficients of your polynomial, as you have done. Interpolation is sort of related, but I think you more want to know how to find the polynomial itself. Yes, this sort of thing is very well researched and applies to polynomials of any degree, and all sorts of other problems. As the number of equations get large, we have more "automated" ways of solving a system of equations, such as Gaussian elimination. - Rainwarrior ( talk) 05:33, 18 January 2008 (UTC)
first of al this isnt my homework question..!! so plz help me solve this question of fuji film.. it is for my own personal understanding....!! plz try and help me answer all questions..i have been trying to solve it since 3 days but aint gettin newhere m typing down the whole case here..
In the early 1990s, Fuji Photo Film, USA, joined forces with four of its rivals to create the Advanced Photo System (APS), which is hailed as the first major development in the film industry since 35 - millimeter technology was introduced. In February 1996, the new 24 millimeter system, promising clearer and sharper pictures, was launched. By the end of the year, the lack of communications and a limited supply of products made retailers angry and consumers baffled. Advertising was almost nonexistent. Because the product was developed by five industry rivals, the companies had enacted a secrecy agreement in which no one outside of company management, including the company's sales force, would know details about the product until each company introduced its APS products on the same day. When the product was actually introduced, it came with little communication to retailers about the product, virtually no training of sales representatives on the product ( so that they could demonstrate and explain the features ), and a great underestimation of demand for the product. Fortunately, Fuji pressed on by taking an "honesty is the best policy" stance and explaining to retailers and other costumers what had happened and asking for patience. In addition, Fuji increased its research to better ascertain market positioning and size. By 1997, Fuji had geared up production to meet the demand and was increasing customer promotion. APS products were on the road for success. By 1998, APS cameras owned 20% of the point and shoot camera market.
1. As stated, by 1998 APS cameras owned 20% of the point and shoot camera market. Now it is the year 2003 and the market share might be nearer to 40%. Suppose 30 cusomers from the point and shoot camera market are randomly selected. If the market share is really .40 , what is the expected number of point and shoot camera customers who purchase an APS camera? What is the probability that six or fewer purchases and APS camera? Suppose you actually got six or fewer APS customers in the sample of 30. Based on the probability just calculated, is this enogh evidence to convince you that the market share is 40% Why or why not?
2. Suppose customer complaints on the 24 millimeter film are poison distributed at an avegare rate of 2.4 complaints/100,000 rols sold. Suppose further that Fuji is having trouble with shipments being late and one batch of 100,000 rolls yields seven complaints from customers. Assuming that it is unacceptable to management for the average rate of complaints to increase, is this enough evidence to convince management that the average rate of complaints has increased, or can it be written off as a random occurence that happens quite frequently? Produce the Poisson distribution for this question and discuss its inplication for this problem.
3. One study of 52 product launches found that those undertaken with revenue growth as tha main objective are more likely to fail than those undertaken to increase customer satisfaction or to create a new market such as the APS system. Suppose of the 52 products launched, 34 were launched with revenue growth as the main objective and the rest were launched to increase cusotmer satisfaction or to create a new market. Now suppose only 10 of these products were successful ( the rest failed) and seven were products that were launched to increase customer satisfaction or to create a new market. What is the probability of this result occuring by chance? What does this probability tell you about the basic premise regarding the importance of the main objective? —Preceding unsigned comment added by 220.225.79.210 ( talk) 14:00, 18 January 2008 (UTC)
I need to know how many gigabytes is 153.44 megabytes and any many gigabytes is 4812 kilobytes? Thanks!
71.145.168.69 ( talk) 17:24, 18 January 2008 (UTC)