The waiting time W for accessing one record from a computer database is a random
ID: 3219663 • Letter: T
Question
The waiting time W for accessing one record from a computer database is a random variable uniformly distributed between 0 and 28 milliseconds.
The read time R for moving the information from the disk to the main memory is 7 milliseconds.
The random variable X milliseconds is the total access time (waiting time + read time) to get one block of information from the disk.
Before performing a certain task, the computer must access 6 different blocks of information from the disk. (Access times for different blocks are independent of one another.)
The total access time for all the information is a random variable A milliseconds.
Compute the following: (a) EX] ar X o A Now use the central limit theorem to estimate the following probabilities. (e) PLA 144 PIA 105)Explanation / Answer
X is composed of read time R of 7 milliseconds and a uniform variable W distributed between 0 and 28
here a=0,b=28
a)E(X) = E(R) +E(W) = 7 + (28-0)/2 = 21
Var(x) = Var(W) (R is constant)
b)Var(x) = (28-0)^2 / 12 = 65.33
Sigma(x) = Sqrt(65.33) = 8.082
E(A) = n*E(x) where n = 6
c)E(A) = 6*21= 126
d)Sigma(W) = Sqrt(n) * Sigma(x) = sqrt(6)* 8.082 = 19.7989
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