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 that fxy (x, y) is a joint probability density function.Round your answers to three decimal places (e.g. 98.765).Determine the following: (d) E(Y) =(e) For 0 < x < 1 marginal probability distribution of X isO x- 1-for 0 < x < 1;-for 1

Answered: Image /qna-images/answer/03d6afaa-badb-442d-801d-7b6ab80a56af.jpg

Answered: (d) E(Y) = (e) For 0 < x < 1 marginal…

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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Find the critical value of t for a t-distribution with 30 degrees of freedom such that the area between −t and t is 99%.
The random variables X and Y have the joint density: fX,Y(x,y) = 2−x−y, for 0<x<1, 0<y<1 0, otherwise For each of the following, please provide your answers in three decimal places: (a) What is the expected value of X? (b) What is the variance of X? (c) What is the covariance of X and Y? (d) What is the correlation of X and Y?
let X and Y are two random variables with p.d.f as f(x,y)=3x2y+3yx2 0<x<1 0<x<1.find conditional density of X given Y?.Find mean mode and standard deviation of r.v Y?. Correlation between X and Y?. check that X and Y are independent or not?.
Suppose that X, Y , and Z are random variables with a joint density f(x, y, z) = ( 6/((1+x+y+z)^4)) , when x, y, z > 0, and 0, otherwise. Determine the distribution of X + Y + Z.
D.1.2 Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.13, and 9.8 liters. Use α 0.01 level of significance and assume that the distribution of contents is normal.
The joint PDF of the random variables X and Y is constant on the region (x,y):x≥0∩yleq1∩−0.5≤x−y≤0, shown in the image below, and is zero outside. Determine P(Y>0.5|X<0.5)
The article “Wastewater Treatment Sludge as a Raw Material for the Production of Bacillus thuringiensis Based Biopesticides” (M. Tirado Montiel, R. Tyagi, and J. Valero, Water Research, 2001:3807–3816) presents measurements of total solids, in g/L, for seven sludge specimens. The results (rounded to the nearest gram) are 20, 5, 25, 43, 24, 21, and 32. Assume the distribution of total solids is approximately symmetric. a) Can you conclude that the mean concentration of total solids is greater than 14 g/L? Compute the appropriate test statistic and find the P-value. b) Can you conclude that the mean concentration of total solids is less than 30 g/L? Compute the appropriate test statistic and find the P-value. c) An environmental engineer claims that the mean concentration of total solids is equal to 18 g/L. Can you conclude that the claim is false?
Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with ? = 4 and ? = 2. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = V(X) = (b) Compute P(X ≤ 0.3). (Round your answer to four decimal places.)(c) Compute P(0.3 ≤ X ≤ 0.7). (Round your answer to four decimal places.)
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