An engineer is measuring a quantity 0. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and report the average of the measurements as the estimated value of 0. Here, n is assumed to be large enough so that the central limit theorem applies. If X, is the value that is obtained in the ith measurement, we assume that X; = 0 + W, where W, is the error in the ith measurement. We assume that the W,'s are i.i.d. with EW, = 0 and Var(") = 4 units. The engineer reports the average of the measurements X, + X2+...+X, X = How many measurements does the engineer need to make until he is 90% sure that the final error is less than 0.25 units? In other words, what should the value of n be such that P(0 – 0.25 < X <0 + 0.25) 2 .90?

An engineer is measuring a quantity 0. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and report the average of the measurements as the estimated value of 0. Here, n is assumed to be large enough so that the central limit theorem applies. If X, is the value that is obtained in the ith measurement, we assume that X; = 0 + W, where W, is the error in the ith measurement. We assume that the W,'s are i.i.d. with EW, = 0 and Var(") = 4 units. The engineer reports the average of the measurements X, + X2+...+X, X = How many measurements does the engineer need to make until he is 90% sure that the final error is less than 0.25 units? In other words, what should the value of n be such that P(0 – 0.25 < X <0 + 0.25) 2 .90?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose that the finite population being studied has N elements from which a sample of size n is drawn using SRSWOR to estimate the population total LOOK AT THE IMAGE ATTACHED
Imagine you have two estimators X and Y, for unknown parameter µ. Assume that they are estimated from independent datasets. Let Z = }(X+Y) be the average of these two estimators. To write the symbol µ, you can write mu. For other math notation, you can E[X], Var(X) and (X+Y)/2 or (1/2)(X+Y). Part a - If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short derivation. Part bL Assume Var(X) = Var(Y). Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.
A medical researcher says that less than 82% of adults in a certain country think that healthy children should be required to be vaccinated. In a randon sample of 300 adults in that country, 78% think that healthy children should be required to be vaccinated. At a = 0.10, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and Ha Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) CA. Less than 82 % of adults in the country think that healthy children should be required to be vaccinated. O B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not %. O C. More than % of adults in the country think that healthy children should be required to be vaccinated. O D. % of adults in the country think that healthy children should be required…
If S = {a,b,c} with P(a) = P(b) and P(c) = 0.24, find P(a). (Enter answer as a decimal with at least 2 correct decimal places)
Hi, i have one question. How was the level of significance obtained? at the beginning of the exercise it is clarified that it is (α)=0.05 but I don't know where this value comes from
3. Let X1, and E- X; are independent. , Xn be iid with exponential distribution with mean 0. Show that (X1+X2)/ E=1 X;
There is always a claim that after measles immunization, children develop hightemperature. A researcher at IHK was interested in finding out the validity of thisclaim. On a designated immunization day, he randomly selected 5 children (withnormal temperature before being immunization). He measured their temperatureagain 6 hours after being immunized against measles. The following were theirtemperatures in (0C): 37.7, 36.7, 39.3, 38.2 and 35.9.a) Is there evidence that the measles vaccine leads to increase in a child’s temperaturefrom the normal temperature of 36.7 (0C)?
Amedical researcher says that less than 79% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 75% think that healthy children should be required to be vaccinated. At a= 0.01, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below SE (a) Identify the claim and state H, and H,. ome Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) ents O A. Less than % of adults in the country think that healthy children should be required to be vaccinated. ok O B. More than % of adults in the country think that healthy children should be required to be vaccinated. Contents C. %% of adults in the country think that healthy children should be required to be vaccinated. O D. The percentage of adults in the country who think that healthy children should be…
Ex. Given a random sample of size n from a gamma populatin. use the method of moments to obtain formulas for estimating th parameters a and B.
I would like all parts for E, ( i, ii, iii, iv v, vi) to be answered please Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling differentdistances, due to cornering, braking and wheel alignment. Manufacturers of car tyresare interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need tobe replaced. At this time a tyre is considered unroadworthy. E) The lifetime T in thousands of km of brand E of car tyres, satisfies a probability density function given by. f(t)=(at^2 0=t=50, b(100-t) 50=t=100, 0 elsewhere) i) Show that a = 3/312500 and b= 3/6250 ii) For 36 tyres of brand E, find the expected number that will last longer than 40,000 km. iii)Sketch the graph of T on the axes below, clearly labelling the scale. iv) Find the expected value and variance of brand E car tyres. v) Find the probability that the lifetime of brand E car tyres lies within two standard…
Chapters: Normal and Exponential random variables. Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.
Kelvin’s bookcase holds 2 algebra books, 1 calculus book, and 4 geometry books. Books are taken at random from his bookcase, one after another and without replacement, until a geometry book is had, at which point no more books are taken. The random variable Y represents the total number of books taken during this experiment. Find Pr[ Y = 3 ].