a.
Find
a.
Answer to Problem 19E
The value of
Explanation of Solution
Given info:
The joint probability density
Calculation:
The formula for finding
The value of
Thus, the value of
For
From Exercise 18,
The formula for finding
Therefore,
Thus, the Thus, the value of
For
From exercise 18,
The formula for finding
Therefore,
Thus, the Thus, the value of
Now
Thus, the value of
b.
Find the value of
b.
Answer to Problem 19E
The value of
Explanation of Solution
Calculation:
The formula for finding the
From part (a), the value of
The formula for finding
Therefore,
Thus, the Thus, the value of
The formula for finding
Therefore,
Thus, the Thus, the value of
Substitute
Thus, the value of
c.
Find the conditional probability density function
c.
Answer to Problem 19E
The conditional probability density function
Explanation of Solution
Calculation:
The formula for finding
The value of
The value of
Now the conditional probability density function
Thus, the conditional probability density function
d.
Find the conditional expectation
d.
Answer to Problem 19E
The conditional expectation
Explanation of Solution
Calculation:
The formula for finding
From part (c), the conditional probability density function
Therefore,
Thus, the conditional expectation
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Chapter 2 Solutions
Statistics for Engineers and Scientists
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- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,