(e) For 0 < x < 1 marginal probability distribution of X isОх-116,-for 0 < x < 1;for 1 < x < 4; 0elsewhere457.5O 2for 0 < x < 1;-for 1 < x < 4; 0elsewhere151345O x+1-for 0 < x < 1;¬nfor 1 < x < 4;Oelsewhere12O x+1for 0 < x < 1;-7.54-for 1 < x < 4;0 elsewhere15114-for 0 < x < 1;for 1 < x < 4; 0elsewhere1545 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, fry (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 =i0.133(a) P(X < 0.6, Y < 0.7) =i(b) P(X < 0.6) =i(c) E(X) =i(d) E(Y) =i

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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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Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid fx\p(x |p) = (1 – p)*-'p x-1 X1, X2, for 0
pls answer d,e,f on paper and draw the criitical region (D) pls use paper but dont use excel
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Exercise 1. Suppose that X ~ N(7, 2.25). Data x is an observed IID sample of size n = 500 from the distribution of X. That is, the IID Data Model is: x + X, where X - IID(500) X IID(500) N(7,2.25). (a) Give a rough sketch of your guess at the density histogram of data x, including labeled tick marks on the horizontal axis. Explain why you expect the density histogram of the data x to look this way. (b) The sample mean x and the sample variance s2 of these 500 data values were computed. What would you guess their values are and why? (c) How many (give a count, not a percentage) of the 500 data values in x would you guess are less than 6? Explain why you believe your guess should be reasonable.
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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, fxy(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: b) E(Y|X=2)= c) P(Y<2.1|X=2)=
pls answer d,e,f and pls draw the critical region (d) write on paper pls and dont use excel
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.
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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].

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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