a) Let X₁, X2,..., Xn denote a random sample from N(0, 2) distribution withprobability density function:f(x; σ²)=1O√2πx²e 20² -∞0 < x < 00And let S² = Σ1x7be the estimator of ².ni) Show whether or not that S² is an unbiased estimator of o²?ii) Show that S² is a consistent estimator of o².

X~N(0, standard deviations σ2)

Answered: a) Let X₁, X₂, X, denote a random…

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 = ((X1,Y1),...,(X, Yn)) be a sample from a bivariate normal population. Show that the distributions of X form a five-parameter exponential family and identify п, В, Г, and h.
A probability distribution function is modeled by the following X-Y cartesian graph: 15k 长 6 7 12 Determine the following: 1. Probability density function for the intervals defined on the graph. 2. Expected value of X. 3. Variance of X. I 4. P(X<5) 5. P(2
Consider the probability density function P. (x) = a e-b lxl where X is the random variable which assum es all the values from - ∞ to o. Find CDr ) 4.
Let X and Y be independent random variables with the distributions X ∼ Geometric(p = 1/3)and Y ∼ Geometric(p = 2/3). Find Pr[X = Y].
Let X equal the IQ of a randomly selected American. Assume X ~ N( μ μ {"version":"1.1","math":"μ"} =100, σ σ {"version":"1.1","math":"σ"} =4). What is the probability that a randomly selected American has an IQ below 90?
Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)
Let x1, x2, ..., n represent a random sample from a distribution with mean E(x) and variance Var(x). Show that Cov(x, x₁ - x) = 0.
Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.
The time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let T1 and T2 be two independent waiting times for this distribution. Find expected time between each call and variance. (E(T) and V(T)) Find the probability for both T1 and T2 to be greater than one.
b) Let Y,,Y2, .. , Yn denote a random sample from N(0,0) distribution with probability density function: f(y;8) = e V2n0 i) Show that f(y; 0) belongs to the 1-parameter exponential family. ii) What is the complete sufficient statistic for 0? Justify your answer. iii) Show whether or not, the maximum likelihood estimator is an unbiased estimator of 0. iv) Does the estimator attains the minimum variance unbiased estimator of 0.
Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is either +1 or −1. State the conditions which make the correlation equal to +1.

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