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of measuring surface smoothne nal surface smoothness in code ver the region 0 < x < 4,0 < h that fay (x, y) is a joint probat

of measuring surface smoothne nal surface smoothness in code ver the region 0 < x < 4,0 < h that fay (x, y) is a joint probat

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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, fay (x, y) = c for xand yin the region. Determine the value for c such that fsy (x, y) is a joint probability density function. Round your answers to three decimal places (e.g. 98.765). Determine the following: c = i (a) P(X < 0.8, Y < 0.6) = i (b) P(X < 0.8) = i (c) E(X) = i (d) E(Y) = i (e) For 0 < x< 1 marginal probability distribution of X is O x+1 for 0 < x < 1;- 2 for 1 <x < 4; 0elsewhere 11 for 0 <x < 1;for 1 <x < 4;0elsewhere 15 45 x +1 for 0 < x< 1;- for 1 <x < 4;0elsewhere 7.5 4 O 2 13 for 0 < x < 1;for 1 < x < 4; 0elsewhere x - 1 16 for 0 < x < 1;for 1 <x < 4; 0elsewhere 7.5 45for
Transcribed Image Text: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 xand yin the region. Determine the value for c such that fsy (x, y) is a joint probability density function. Round your answers to three decimal places (e.g. 98.765). Determine the following: c = i (a) P(X < 0.8, Y < 0.6) = i (b) P(X < 0.8) = i (c) E(X) = i (d) E(Y) = i (e) For 0 < x< 1 marginal probability distribution of X is O x+1 for 0 < x < 1;- 2 for 1 <x < 4; 0elsewhere 11 for 0 <x < 1;for 1 <x < 4;0elsewhere 15 45 x +1 for 0 < x< 1;- for 1 <x < 4;0elsewhere 7.5 4 O 2 13 for 0 < x < 1;for 1 < x < 4; 0elsewhere x - 1 16 for 0 < x < 1;for 1 <x < 4; 0elsewhere 7.5 45for
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