Show that any uncorrelated Gaussian random variables are statistically independent.

Answered: Image /qna-images/answer/bc87fc3d-545d-46eb-a748-245039359172.jpg

Answered: Show that any uncorrelated Gaussian…

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

5
A cellular call is made to your cell phone at random within a ten-minute interval. You werebusy on a call for 2 minutes into this ten-minute period. There is a probability that the callarrived when you were not busy on your cell. Identify the random variable and define thedistribution of the random variable?
A company is introducing a new product. It has 100 retail locations each independently agreeing to offer it with probability 0.2. The amount of sales of the new product in each location is a normal random variable with average 100 and standard deviation 15. Calculate the expectation of the total sales of the new product. Calculate the variance of the total sales of the new product.
I asked this question before, and got an answer, but I have a question about the response that was given. The original question was: For an initial investment of 100, an investment yields returns of X1 and X2, where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability that the rate of return of this investment is greater than 10%? In the answer that was given it says that the gain of the investment is X1+X2. My question is why can we just group those together as one amount? I was given a formula in my class that says the return on the investment would be the solution to the equation: -100+ X1/(1+r) + X2/(1+r)2=0. If this formula is used, a different solution would result for this problem.
A computer repair shop has two work centers. The first center examines the computer to see what is wrong and the second center repairs the computer. Let and be random variables representing the lengths of time in minutes to examine a computer () and to repair a computer (). Assume and are independent random variables. Long-term history has shown the following mean and standard deviation for the two work centers: Examine computer, : = 27.3 minutes; = 7.5 minutes Repair computer, : = 90.1 minutes; = 15.3 minutes Let be a random variable representing the total time to examine and repair the computer. Suppose it costs $1.80 per minute to examine the computer and $2.83 per minute to repair the computer. Then is a random variable representing the service charges (without parts). Compute the mean and standard deviation of V. Round your answer to the nearest tenth.
One common disease among pediatric patients is streptococcal pharyngitis (strep throat). If a pediatric patient comes in to the pediatricians feeling ill, there is a 26% chance that they have strep throat. A doctor sees 7 pediatric patients on a particular day (assume these patients are independent). Consider the random variable is a binomial random variable such that X = number of pediatric patients with strep throat. What is the expected number of pediatric patients with strep throat?
Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 107 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities:
Let X be a chi-squared random variable with 12 degrees of freedom. What is the probability that X is greater than 23? What are the steps to come to this conclusion?
A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.
Female undergraduates in randomized groups of 15 took part in a self-esteem study. The study measured an index of self-esteem from the point of view of competence, social acceptance, and physical attractiveness. Let x1, x2, and x3 be random variables representing the measure of self-esteem through x1 (competence), x2 (social acceptance), and x3 (attractiveness). Higher index values mean a more positive influence on self- esteem. Variable Sample Mean Standard Deviation Population Size Мean 15 19.48 2.92 X1 X2 X3 (a) Find a 90% confidence interval for u1 - 42. (Round your answers to two decimal places.) lower limit 15 19.90 3.98 H2 15 17.42 3.60 upper limit (b) Find a 90% confidence interval for u1 - 43. (Round your answers to two decimal places.) lower limit upper limit (c) Find a 90% confidence interval for u2 - 13. (Round your answers to two decimal places.) lower limit upper limit
which of the following random variables isn't discrete? (a) the number of children in a family (b) the annual rainfall in a city (c) the attendance at a football game (d) the number of patients treated at an emergency room in a day (e) the number of classes taken in one semester by a student

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