7. For a bivariate normal distribution with \( \mu_X, \mu_Y, \sigma_X^2 > 0, \sigma_Y^2 > 0 \) and \( |\rho| < 1 \),(a) Find the conditional density for \( X|Y = y \).(b) Determine the distribution of\[\frac{X^2 - 2\rho XY + Y^2}{1 - \rho^2}\]when \( \mu_X = \mu_Y = 0 \) and \( \sigma_X^2 = \sigma_Y^2 = 1 \).

Answered: Image /qna-images/answer/e838b6aa-a23c-480d-a6d2-3c999dc44537.jpg

Answered: 7. For a bivariate normal distribution…

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

3. Find the boundary that corresponds the the probability for the standard normal distribution. (a) P(z< zo) = 0.8203 (b) P(zo < z) = 0.8997 4. Find the boundary that corresponds the the probability for the normal distribution. (a) P(x < xo) = 0.8203 when µ„ = 25 and op = 6.5 (b) P(yo < y) = 0.8997 when ly = 25 and oy = 6.5
The pressure of air (in MPa) entering a compressor is measured to be X = 8.5 ± 0.2, and the pressure of the air leaving the compressor is measured to be Y = 21.2 ± 0.3. The intermediate pressure is therefore measured to be P = √XY = 13.42 . Assume that X and Y come from normal populations and are unbiased. a) From what distributions is it appropriate to simulate values X* and Y*? b) Generate simulated samples of values X*, Y*, and P*. c) Use the simulated sample to estimate the standard deviation of P. d) Construct a normal probability plot for the values P*. Is it reasonable to assume that P is approximately normally distributed? e) If appropriate, use the normal curve to find a 95% confidence interval for the intermediate pressure.
3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentile
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630
7. If the r.v.'s X and Y have bivariate normal distribution with parameters ₁ = 3.2, µ2 = 1.44, 0₁ = 12, 02 = 16 and p = 0.7, determine the following quantities: (a) E(X), E(Y), Var(X), Var(Y), p(X, Y), and Cov(X, Y). (b) the distribution of X and the distribution of Y. (c) the probabilities P(0.8 14). (d) the conditional distribution of Y, given X = 3.8. (e) the conditional distribution of X, given X = 10. (f) the probabilities P(X > 3.2|Y = 10), P(Y < 12|X = 3.8). (g) E(X|Y = 10), E(Y|X = 3.8), Var(X|Y = 10), Var(Y|X = 3.8).

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

7. For a bivariate normal distribution with µx,µy,o} > 0,0² > 0 and |p| < 1, (a) Find the conditional density for X Y = y. (b) Determine the distribution of X² − 2pXY+Y² 1 - p² = 1. when μx = μy = 0 and o =