1) Suppose tha Y is a random variable having an gamma distribution with a = 1, findthe value of k such that an interval from 0 to ky is a(1 - a) 100% confidence interval for the parameter B.

Answered: 1) Suppose tha Y is a random variable…

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

Let X. X , be a random sample of siren from a normal distribution with population mean 0 and population variance a>Ois unknown, that is N(0, ). Suppose that we define the following plvotal quantity (n-1)s where & and S' are the sample mean and the sample variance, respectively. Use the plvotal quantity (Q) to derive the (1- a) 100% confidence interval (C) for the unknown parameter (o) if the two critical values are q--n, a) and (n-1) (A) CI = (n8+(n-1)51 + n-1) s (8) CI - (C) CI - + (n-1) s (D) CI= O D O A O c O B
Consider the performance function Y= 2X1-2X2+8X3 are all normally distributed random variables with μΧ1 = 10.4 ; μΧ2 = 11.8 ; μΧ3= 11.5Vx1 = 4 % , Vx2 = 5% ; Vx3 = 8 % X1 X2 X3q = 1 0,8 6 X1 0,8 1 0,5 X2 -----> correlation of Matrix 0,6 0,5 1 X3 Y < 0; failure occurs 15 simulations Pf =? . Determine the probability of failure ? (Reliability of Structures)
Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 0
6). A random sample of 90 observations produced a mean of x¯=21 from a population with a normal distribution and a standard deviation σ=4.1.
Suppose X is a random variable with standard beta distribution and parameters (alpha) = 8 and (beta) = 2 What is (PX>=0.6)?
11. Consider a random sample Y₁, Y2, ..., Yn from a normal population Y~N(μ, o²) where the population variance and mean are unknown. We want to construct a Σ(X-X)² Show 100(1 a)% confidence interval for the population variance if g² whether or not is a pivotal quantity and construct a 100(1-a) confidence interval.
A random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?
(Mathematical Statistics) Let X1,X2,...,X5 be a random sample of the Gamma distribution with parameters a = and ß = 0, e > 0. Determine the 95% confidence interval for the parameter e based on the statistic E(i=1 - 5) Xi. 2
Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that ɛ P(X - ≤ μµ)≈ 0.95.
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, ×, is found to be 110, and the sample standard deviation, s, is found to be 8. (a) Construct a 99% confidence interval about u if the sample size, n, is 24. (b) Construct a 99% confidence interval about u if the sample size, n, is 13. (c) Construct a 96% confidence interval about u if the sample size, n, is 24. (d) Should the confidence intervals in parts (a)(c) have been computed if the population had not been normally distributed? An example was provided with additional pictures.
3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be two estimates of u. * Which of these two estimators is unbiased? * Which is the better estimator, and why? %3D
IF n < 30 AND T = Ý−µ -H, √n SHOW HOW THE 100(1-2x)% CONFIDENCE INTERVAL FOR U IS DERIVED

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

1) Suppose tha Y is a random variable having an gamma distribution with the value of k such that an interval from 0 to ky is a (1-a) 100% confidence interval for the parameter B.