Suppose 1, 2, ... are iid random variables having mean u and variance o2. Form the randomsum SN = $1 +:+ EN....(a) Derive the mean and variance of SN when N has a Poisson distribution with parameterA.(b) Determine the mean and variance of SN where N has a gcometric distributions with mean(c) Compare the behaviors in (a) and (b) as A→ oo.

Answered: Image /qna-images/answer/b0f7d642-4675-4fd4-b1f1-5978b4ebda50.jpg

Answered: sum SN $1 +..+ EN. %3D (a) Derive the…

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

1. Let X have the pdf f(x) = B-lexp{-x/B}, 0 < x
Time left 0:08:09 On average, a milk packaging machine fills milk into 1000 milliliter-packages. Sometimes, the machine makes errors with an estimated variance of 400. What is the z-score for a randomly selected milk package that measured 910 milliliters? [Give your answer correct to 1 decimal place] Answer: Next page
4
a, b, d,
X and Y are independent
A1
f(x) = (2x + 1)/c, 0 ≤ x ≤ 4. Find the variance of the distribution. 438/c² 409.2/c² O 431.6/c² O 419.6/c²
The time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.
Q.6 (a) Write the gamma distribution for a random variable X denoted by X~F(a, B); its mean, variance and moment generating function (No derivation is required). (b) What is the relationship between gamma distribution and chi-square distribution?
1. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwise
A technician suspect that the number of computer errors recorded per day in the LAN follows a Poisson distribution with a mean of 2 errors per day. Record of the number of errors per day for the past 260 days are shown in table below. Number of Number of Pr(X = x) E (0; – e;) Errors per days ei day 77 1 90 2 55 3 30 4 or more a. Test the hypothesis that the number of computer errors per day has the Poisson distribution with mean 2 at the 5% significance level. b. Find an approximate value of the p – value for the test statistics in (a). 8
Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?

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

sum SN $1 +..+ EN. %3D (a) Derive the mcan and variance of SN when N has a Poisson distribution with parameter A. (b) Determine the mean and variance of SN where N has a geometric distributions with mean (c) Compare the behaviors in (a) and (b) as X 0o.