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.
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.
Compute
Answer to Problem 98SE
The value of
Explanation of Solution
Calculation:
The value of
Thus, the value of
c.
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.
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
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