5 6) Consider the random variable Zn = cos(2 * T * "n/n) where Yn is binomial(n,p)a. What is its asymptotic variance for arbitrary p as n increasesb. What happens at p=1/2Write an r program that shows you graphical the (simulated) standard deviation of Znvs 1/sqrt(n) as n increases for different values of p including 0.5C.

The given question focuses on analyzing the properties of a random variable defined as , which is…

Answered: 6) Consider the random variable Z₁ =…

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 the distribution of the time $X$ (in hours) spent by students at a certain university on a particular project is gamma with parameters $\alpha=50$ and $\beta=2 .$ Because $\alpha$ is large, it can be shown that $X$ has approximately a normal distribution. Use this fact to compute the approximate probability that a randomly selected student spends at most 125 hours on the project.
Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero elsewhere. what is variance of this random variable?
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?
Let Zw distributed as Chi square random variable with n degree of freedom. Find the limiting distribution of Wn = Zw/n2
A simple random sample of size n =66, is obtained from a population that is skewed left with =33 and =3. . Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?(A) Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (B) Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. (C)No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x, become approximately normal as the sample size, n, increases. (D) No. The central limit theorem…
Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.61 and standard deviation 0.76. (a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? (Round your answers to four decimal places.) (b)Between 2.61 and 3.00? (Round your answers to four decimal places.)(c) How large a sample size would be required to ensure that the first probability in part (a) is at least 0.99?
1. Let X be a Poisson random variable with E[X] = ln2. Calculate E[cosπX]. 2. The number of home runs in a baseball game is assumed to have a Poisson distribution with a mean of 3. As a promotion, Mall A pledges to donate 10,000 dollars to charity for each home run hit up to a maximum of 3. Find the expected amount that the company will donate. Mall B also X dollars for each home run over 3 hits during the game, and X is chosen so that the Mall B's expected donation is the same as the Mall A's. Find X.
Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
Consider random variables X1, · · · Xn, independent and identically distributed such that each Xi ∼N (0, 1). Write down an expression for the joint pdf of the n-dimensional random vector (X1, · · · Xn).(i.e. what is the distribution of a random sample of n standard normal random variables
Suppose that a random sample from a normal popula-tion with the known variance σ2 is to be used to test the null hypothesis μ = μ0 against the alternative hypothe-sis μ = μ1, where μ1 > μ0, and that the probabilities of type I and type II errors are to have the preassigned val-ues α and β. Show that the required size of the sample is given by n = σ2(zα + zβ)2(μ1 − μ0)2
Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.
The fraction of a bottle that is filled with a particular liquid is a continuous random variable X withpdf f(x; theta)= theta (x^(theta-1)) for 0 < x < 1 (where y > 0).a. Obtain the method of moments estimator for theta.b. Is the estimator of (a) a sufficient statistic? Ifnot, what is a sufficient statistic, and what isan estimator of theta (not necessarily unbiased)based on a sufficient statistic?

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