Concept explainers
a.
Find the joint probability mass
a.
Answer to Problem 25SE
The joint probability mass function of X and Y is,
Y | |||
X | 0 | 1 | 2 |
0 | 0.0667 | 0.2000 | 0.0667 |
1 | 0.2667 | 0.2667 | 0 |
2 | 0.1333 | 0 | 0 |
Explanation of Solution
Given info:
A box contains four 75W light bulbs, three 60W light bulbs, and three burned-out light bulbs. Also, two bulbs are selected at random from the box.
Here, X represents the number of 75W bulbs selected, and let Y represent the number of 60W bulbs selected.
Calculation:
From the given information, it can be observed that the two bulbs are selected random. The number of not burned-out light bulbs is 7
Therefore, the probabilities for finding the joint probability mass function of X and Y is,
For
For
For
For
For
For
By using the above probabilities, the joint probability mass function of X and Y is,
Y | |||
X | 0 | 1 | 2 |
0 | 0.0667 | 0.2000 | 0.0667 |
1 | 0.2667 | 0.2667 | 0 |
2 | 0.1333 | 0 | 0 |
Table 1
b.
Find the value of
b.
Answer to Problem 25SE
The value of
Explanation of Solution
Calculation:
The totals of the joint probability mass function of tensile strength (in thousands of pounds/in2) and additive concentration is,
Y | ||||
X | 0 | 1 | 2 | Total |
0 | 0.0667 | 0.2000 | 0.0667 | 0.3334 |
1 | 0.2667 | 0.2667 | 0 | 0.5334 |
2 | 0.1333 | 0 | 0 | 0.1333 |
Total | 0.4667 | 0.4667 | 0.0667 | 1 |
Table 1
The value of
Thus, the value of
c.
Find the value of
c.
Answer to Problem 25SE
The value of
Explanation of Solution
Calculation:
The value of
Thus, the value of
d.
Find the value of
d.
Answer to Problem 25SE
The value of
Explanation of Solution
Calculation:
The value of
Thus, the value of
The formula for finding
Thus, the value of
e.
Find the value of
e.
Answer to Problem 25SE
The value of
Explanation of Solution
Calculation:
The value of
Thus, the value of
The formula for finding
Thus, the value of
e.
Find the value of
e.
Answer to Problem 25SE
The value of
Explanation of Solution
Calculation:
The value of
Thus, the value of
g.
Find the value of
g.
Answer to Problem 25SE
The value of
Explanation of Solution
Calculation:
The formula for finding the
Substitute
Thus, the value of
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