Solution Found!
Suppose that a table of part counts is generalized as
Chapter 2, Problem 235MEE(choose chapter or problem)
Suppose that a table of part counts is generalized as follows:
where 𝑎, 𝑏, and 𝑘 are positive integers. Let 𝐴 denote the event that a part is from supplier 1, and let 𝐵 denote the event that a part conforms to specifications. Show that 𝐴 and 𝐵 are independent events. This exercise illustrates the result that whenever the rows of a table (with 𝑟 rows and 𝑐 columns) are proportional, an event defined by a row category and an event defined by a column category are independent.
Questions & Answers
QUESTION:
Suppose that a table of part counts is generalized as follows:
where 𝑎, 𝑏, and 𝑘 are positive integers. Let 𝐴 denote the event that a part is from supplier 1, and let 𝐵 denote the event that a part conforms to specifications. Show that 𝐴 and 𝐵 are independent events. This exercise illustrates the result that whenever the rows of a table (with 𝑟 rows and 𝑐 columns) are proportional, an event defined by a row category and an event defined by a column category are independent.
ANSWER:
Solution:
Step 1 of 2:
We have,
Conforms |
||||
Suppliers |
Yes |
No |
Total |
|
1 |
ka |
kb |
K(a+b) |
|
2 |
a |
b |
a+b |
|
Total |
Ka + a |
Kb + b |
Where, a, b, and k are positive integers.
Let, A = part from supplier 1.
B = part conforms to specifications.
AB = events of part supplied by supplier 1 are confirms.
The claim is to show that the event defined by a column category are independent.