a.
Find an expression for
a.
Answer to Problem 112E
The expression for
Explanation of Solution
Note that a random variable is said to be a chi-square distribution with
Consider,
Therefore, it is proved that
Now, substitute
b.
Explain the reason why Part a requires
b.
Explanation of Solution
The answer in Part a has to be satisfied that
Thus, the function
c.
Find an expression for
Find one assumption about
c.
Answer to Problem 112E
The expression for
Explanation of Solution
The answer in Part a is as follows:
Substitute
Therefore, the value of
d.
Use the results in Part a to find an expression for
Identify the value of
d.
Explanation of Solution
The result in Part a is as follows:
Case1:
Substitute
Thus, in this case, one needs to assume the value of
Case 2:
Substitute
Therefore, the value of
Case3:
Substitute
Thus, value of
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Chapter 4 Solutions
Mathematical Statistics with Applications
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forward
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