Q1:BB. Let X and Y have a bivariate normal distribution with parameters u, = 3, ly = 1,0 = 16, o, = 25,%3!and p =Suppose that P(c,

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Answered: Q1:B B. Let X and Y have a bivariate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))
3. Let Y, < Y2 < Y, be the order statistics of 3 independent observations from a distribution with 20th percentile n0.2 = 5. Find P(Y, <5). %3D
The Determine the cumulative distribution function for the distribution. answer please thank you.
This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function 1 p(x) = e (x - 1)?/(202), V 2n 0 where n = 3.14159265... and o and u are constants called the standard deviation and the mean, respectively. Its graph (for o = 1 and u = 2) is shown in the figure. f(x) 0.3 0.2 0.1 3 4 5 With o = 3 and u = 0, approximate p(x) dx. (Round your answer to four decimal places.)
33. If X is a normal variate with mean u and variance X- o? and P - b< .2
A,b,c,d.
3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.
Let X and Y be independent standard normal variates. Obtain the m.g.f. of XY.
Let X be a random variable normally distributed with mean μx 1. Find the mean μy of Y. 2. Find the standard deviation oy of Y. 3. Find the PDF fy of Y and evaluate fy (5). (My, oy, fy (5)) = ___________). = 6 and standard deviation ox = 4. Let Y = 4X + 5.
Example 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 45, and (iii) |X – 30l > 5.

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Q1:B B. Let X and Y have a bivariate normal distribution with parameters ux = 3, ly = 1, o = 16, o, = 25, and p = Suppose that P(c,