(d) E(Y) = (e) For 0 < x < 1 marginal probability distribution of X is 16 -for 0 < x < 1;÷for 1 < x < 4;Oelsewhere 7.5 2 - for 0 < x < 1;for 1 < x < 4; Oelsewhere 15 45 13 45 O x +1 1 -for 0 < x < 1; ¬nfor 1 < x < 4; Oelsewhere 12 2 O x +1 4 for 1 < x < 4;0 elsewhere -for ) < x < 1; 7.5 4 for 0 < x < 1;for 1 < x < 4; Oelsewhere 15 11 15 45
(d) E(Y) = (e) For 0 < x < 1 marginal probability distribution of X is 16 -for 0 < x < 1;÷for 1 < x < 4;Oelsewhere 7.5 2 - for 0 < x < 1;for 1 < x < 4; Oelsewhere 15 45 13 45 O x +1 1 -for 0 < x < 1; ¬nfor 1 < x < 4; Oelsewhere 12 2 O x +1 4 for 1 < x < 4;0 elsewhere -for ) < x < 1; 7.5 4 for 0 < x < 1;for 1 < x < 4; Oelsewhere 15 11 15 45
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
Related questions
Question
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, 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:
Transcribed Image Text:(d) E(Y) =
(e) For 0 < x < 1 marginal probability distribution of X is
O x- 1
-for 0 < x < 1;-for 1 <x < 4;Oelsewhere
7.5
16
45
2
-for 0 < x < 1;for 1 < x < 4; 0elsewhere
15
13
45
O x+1
-for 0 < x < 1;for 1 <x < 4; Oelsewhere
2
1
12
O x+1
for 0 < x < 1;
7.5
4
-for 1 < x < 4;0 elsewhere
15
4
11
-for 0 < x < 1;for 1 < x < 4; 0elsewhere
15
45
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