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3
Discrete Random
Variables and
Probability
Distributions
A redundant array of independent disks (RAID) uses multiple
Chapter Outline physical disk drives as one logical unit in a computer system.
The array can increase performance and robustness to a disk
3-1 Discrete Random Variables failure. Data copies can be written simultaneously to multiple
drives (known as mirroring) to provide immediate backup and
3-2 Probability Distributions and the ability to recover from failures but with less storage capac-
Probability Mass Functions ity than would otherwise be available. Alternatively, to increase
performance, the data can be distributed among multiple disks
3-3 Cumulative Distribution Functions
with only a fraction of the data on each one (known as striping).
3-4 Mean and Variance of a Discrete But a failure to even a single disk can lead to loss of data. An
Random Variable intermediate design is to distribute the source data along with
additional data (known as parity data) across multiple disks.
3-5 Discrete Uniform Distribution With the parity data, the source data can be recovered even with
disk failures. In particular, a RAID 5 design uses striping and
3-6 Binomial Distribution parity to be able to recover the source data if one disk in the
array fails, and a RAID 6 design allows for data recovery even
3-7 Geometric and Negative Binomial if two disks fail. Disk failures due to hardware malfunction are
Distributions
often assumed to be independent with constant probability. With
3-8 Hypergeometric Distribution a large number of disks in an array, the risk of data loss and the
appropriate array design to meet the system performance, avail-
3-9 Poisson Distribution ability, and cost criteria are important. The number of failed
drives can be modeled as a discrete random variable, and the
risk of data loss in a redundant system is only one example of
the use of the topics in this chapter.
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