Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviationsfrom the nominal surface smoothness in coded units. The joint probability distribution of the two measurements is a uniformdistribution over the region 0 < x < 4,0 < y, and x – 1 < y < x + 1. That is, fay (x, y) = c for x and y in the region. Determine thevalue for c such thatfy (x, y) is a joint probability density function.Round your answers to three decimal places (e.g. 98.765).Determine the following:c =b) Conditional probability distribution of Y given X = 2.5O fyx-25) = 0.25for 0 < y < 4; 0 elsewhereO fyix=2.5V) = 0.40for 0 < y < 2.5; 0 elsewhere= 0.40for 2.5 < y < 5.0; 0 elsewhereO fyx=250) = 0.5for 1.5 < y < 3.5; 0elsewhere%3Db) E(Y |X = 2.5) =c) P(Y < 1.8|X = 2.5) =

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Answered: Two methods of measuring surface…

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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The magnitudes of Earthquake and Tsunami are given by the variables of m and n, respectively. Their joint occurrence probability is given by the joint probability mass function as: f (m, n) = A (m2 + n?) for the magnitudes of zero, one, two and three. a) Find the value of the constant A. b) Find the mean value of the joint occurrence function of these magnitudes. c) Determine the marginal distributions of these magnitudes. d) If an earthquake of magnitude 1 occurred, find the probability of having a tsunami of magnitude 2 and greater. e) Determine if the magnitude of earthquake and tsunami are independent random variables. Prove your opinion.
Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviations from the nominal surface smoothness in coded units. The joint probability distribution of the two measurements is a uniform distribution over the region 0 < x < 4,0 < y, and .x – 1 < y < x + 1. That is, fry (x, y) = c for x and y in the region. Determine the value for c such that fxy (x, y) is a joint probability density function. Round your answers to three decimal places (e.g. 98.765). Determine the following:
Consider X and Y are joint distributed with PDFf(x,y)=x+y, 0≤x≤1, 0≤y≤1. (d) Find the marginal distributions of X and Y .(e) Find the conditional distribution of X given Y = y.
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Two high school seniors find themselves with much time and nothing to do. They decide to devise a computer game in which a cursor moves randomly along the x axis between -2 and 2. The game they play is to stop the cursor at random points between -2 and 2 without looking at the screen. Such a game results in a uniform distribution overthe interval between -2 and 2 and resemebles a density curve. The height of the density curve is:
Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurements of each of the two methods. Suppose that the joint p.d.f of X and Y is modeled by fxy (x, y) = c, 0 <x <4, 0<y and x-1 < y <x+1 Determine the value of c. Determine the marginal probability distribution of X. Find also the mean and variance of X. Determine the conditional probability distribution of Y given X=2. Find also the conditional mean and conditional variance of Y given X=2 Check if the measurements of the two methods X and Y are independent. * SHOW COMPLETE SOLUTION WITH GIVEN, REQUIRED, AND SOLUTION. SHOW TABLE OF ILLUSTRATIONS IF NECESSARY.
A machine generates rectangular tiles with randomly varying length (L) and width (W). Let the length follow L ~Gamma(100,10) distribution and the width follow W ~Gamma(50,10) distribution, and define the area of the tile as S = L × W, and its perimeter as Q = 2(L+W). For parts (a-c) below, assume the length and width are independent (i.e. LI W). (a) Show that the expected value of the area is E[S] = 50. (b) Show that the variance of the area is Var[S] = 75.5. (c) Use Chebyshev's inequality to find an upper bound on P(S > 75). For parts (d,e) below, assume the length and width are correlated with Corr(L, W) = -0.5. (d) Show that the expected value of the area is E[S] ~ 49.64645. (e) Find the mean and variance of the perimeter: E[Q] and Var[Q].
Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviations from the nominal surface smoothness in coded units. The joint probability distribution of the two measurements is a uniform distribution over the region 0 < x < 4,0 < y, and x – 1 < y < x+ 1. That is, fay (x, y) = c for x and y in the region. Determine the value for c such that fay (x, y) is a joint probability density function. Round your answers to three decimal places (e.g. 98.765). Determine the following: c = i 0.133 (a) P(X < 0.6, Y < 0.7) = i (b) P(X < 0.6) = i (c) E(X) = i (d) E(Y) = (e) For 0 < x < 1 marginal probability distribution of X is O 2 -for 0
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5. Suppose that two continuous random variables X and Y have joint probability density function A( e + e 2x -) 1sxs2,0sys3 ㅇ elsewhere a. P( 3/2 sXs2, 1 SYS2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0 d. Find the strength of the relationship and interpret the findings.

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