Show the nth degree polynomial that minimizes

Reference no: EM131015144

Let _n=0{Φ_n(x)}^∞ be a family of orthonomal polynomials with respect to the weight function w(x). Show that the n^th degree polynomial that minimizes

_-1∫¹ w(x) (f(x) - p_n(x))² dx

is given by

P_n(x) = _k=0Σⁿ c_k Φ_k(x)

where c_k = _-1∫¹ w(x) f(x) f(x) Φ_k(x).

Hint: Expand the expression you want to minimize.

Reference no: EM131015144

Questions Cloud

National survey of engineering school : A national survey of engineering school graduates indicates that only 10% of them have had a course in statistics. (a) Find the probability that in a random sample of five engineering grad uates exactly two have had a course in statistics.

Length of a filament chosen at random lies : 1. The length of a continuous nylon filament that can be drawn without a break occurring is an exponential random variable with mean 5000 feet. (a) What is the probability that the length of a filament chosen at random lies between 4750 and 55..

Develop service delivery observation skills : Service Journal (20%). The purpose of this journal is to develop service delivery observation skills, apply theory discussed in class to each entry, and to reflect on your learning experiences as a consumer

Problem regarding the machine set value : Machines used to fill food cartons are usually set to slightly overfill the boxes so that the contents will not weigh less than the advertised net weight. This takes into account the fact that the actual weight of each box varies somewhat from th..

Show the nth degree polynomial that minimizes : Let n=0{Φn(x)}∞ be a family of orthonomal polynomials with respect to the weight function w(x). Show that the nth degree polynomial that minimizes.

How do copayments and deductibles reduce risk : What are the advantages and disadvantages of ABC relative to the step-down method of cost allocation?

Normal probability plot of the data : 1. Using the hardness data from the odor data set odor .txt, do the following. (a) Make a normal probability plot of the data. (b) Do the data appear to be normally distributed? Explain.

Differentiating the distribution function of a weib : By differentiating the distribution function of a WEIB( 8,,6) random variable (equation (4.3.28) ), show that its density is given by equation (4.3.29).

Discuss whether entering a transaction in a journal : A journal is used to chronologically record all transactions of a business. These transactions are then posted to the ledger. Consider the steps involved in recording transactions in the books of account and respond to the following: Discuss wheth..

User Account

All Pages