JOINT DISTRIBUTIONS 181 TABLE 5.5 xly 3 4 0. 0. 0. 1/35 1 12/35 0. 0. 18/35 010 4/35 0. 2. In conducting an experiment in the laboratory, temperature gauges are to be used at four junction points in the equipment setup. These four gauges are ran- domly selected from a bin containing seven such gauges. Unknown to the sci- entist, three of the seven gauges give improper temperature readings. Let X denote the number of defective gauges selected and Y the number of nondefec- tive gauges selected. The joint density for (X, Y) is given in Table 5.5. o (a) The values given in Table 5.5 can be derived by realizing that the random variable X is hypergeometric. Use the results of Sec. 3.7 to verify the val- ues given in Table 5.5. (b) Find the marginal densities for both X and Y. What type of random variable is Y? (c) Intuitively speaking, are X and Y independent? Justify your answer mathe- matically. 3. The joint density for (X, Y) is given by fxy (x, y) = 1/n² x = 1, 2, 3, . . .,n y = 1, 2, 3, . .., n (a) Verify that fyy (x, y) satisfies the conditions necessary to be a density. (b) Find the marginal densities for X and Y. (c) Are X and Y independent? . The joint density for (X, Y) is given by
JOINT DISTRIBUTIONS 181 TABLE 5.5 xly 3 4 0. 0. 0. 1/35 1 12/35 0. 0. 18/35 010 4/35 0. 2. In conducting an experiment in the laboratory, temperature gauges are to be used at four junction points in the equipment setup. These four gauges are ran- domly selected from a bin containing seven such gauges. Unknown to the sci- entist, three of the seven gauges give improper temperature readings. Let X denote the number of defective gauges selected and Y the number of nondefec- tive gauges selected. The joint density for (X, Y) is given in Table 5.5. o (a) The values given in Table 5.5 can be derived by realizing that the random variable X is hypergeometric. Use the results of Sec. 3.7 to verify the val- ues given in Table 5.5. (b) Find the marginal densities for both X and Y. What type of random variable is Y? (c) Intuitively speaking, are X and Y independent? Justify your answer mathe- matically. 3. The joint density for (X, Y) is given by fxy (x, y) = 1/n² x = 1, 2, 3, . . .,n y = 1, 2, 3, . .., n (a) Verify that fyy (x, y) satisfies the conditions necessary to be a density. (b) Find the marginal densities for X and Y. (c) Are X and Y independent? . The joint density for (X, Y) is given by
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...
Related questions
Concept explainers
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Topic Video
Question
100%
#2 part b and c
Transcribed Image Text:JOINT DISTRIBUTIONS 181
TABLE 5.5
xly
3
4
0.
0.
0.
1/35
1
12/35
0.
0.
18/35
010
4/35
0.
2. In conducting an experiment in the laboratory, temperature gauges are to be
used at four junction points in the equipment setup. These four gauges are ran-
domly selected from a bin containing seven such gauges. Unknown to the sci-
entist, three of the seven gauges give improper temperature readings. Let X
denote the number of defective gauges selected and Y the number of nondefec-
tive gauges selected. The joint density for (X, Y) is given in Table 5.5.
o (a) The values given in Table 5.5 can be derived by realizing that the random
variable X is hypergeometric. Use the results of Sec. 3.7 to verify the val-
ues given in Table 5.5.
(b) Find the marginal densities for both X and Y. What type of random variable
is Y?
(c) Intuitively speaking, are X and Y independent? Justify your answer mathe-
matically.
3. The joint density for (X, Y) is given by
fxy (x, y) = 1/n²
x = 1, 2, 3, . . .,n
y = 1, 2, 3, . .., n
(a) Verify that fyy (x, y) satisfies the conditions necessary to be a density.
(b) Find the marginal densities for X and Y.
(c) Are X and Y independent?
. The joint density for (X, Y) is given by
<r<n.
na positive integer
2.
00000
23
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON