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Concept explainers
Let X = the time it takes a read/write head to locate a desired record on a computer disk memory device once the head has been positioned over the correct track. If the disks rotate once every 25 millisec, a reasonable assumption is that X is uniformly distributed on the interval [0, 25].
a. Compute P(10 ≤ X ≤ 20).
b. Compute P(X ≥ 10).
c. Obtain the cdf F(X).
d. Compute E(X) and σX.
a.
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Compute
Answer to Problem 98SE
The value of
Explanation of Solution
Given info:
The time taken to read/write head to locate the record on a computer disk memory device over the correct track follows uniform distribution in
Calculation:
The probability density function of uniform distribution is given below:
The probability density function of uniform distribution for the interval
The value of
Thus, the value of
b.
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Compute
Answer to Problem 98SE
The value of
Explanation of Solution
Calculation:
The value of
Thus, the value of
c.
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Obtain cumulative density function of
Answer to Problem 98SE
The cumulative density function
Explanation of Solution
Calculation:
The cumulative density function of uniform distribution is given below:
The cumulative density function
The random variable X is uniformly distributed over
For
Since the range of
For
Since the range of
For
Thus, the cumulative density function
d.
![Check Mark](/static/check-mark.png)
Compute
Answer to Problem 98SE
The value of
The value of
Explanation of Solution
Calculation:
The mean of the uniform distribution is given below:
Substitute
Thus, the value of
The
The variance of the uniform distribution is given below:
Substitute
The standard deviation is obtained as given below:
Thus, the value of
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Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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