The waiting time W for accessing one record from a computer database is a random

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 9 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) E[X] = (b) Var[X] = (c) E[A] = (d) sigma_A = Now use the central limit theorem to estimate the following probabilities. (e) P[A > 216] = (f) P[A

Explanation / Answer

(a) E[X] = 7 + (28 + 0)/2 = 21 milli seconds

Here X = Waiting time + read time where waiting time varies as per random distribution and read time doesn't vary so it is in the form of X = R + W , where R is constant and W is variable.

(b) Var[X] = Var [W] = ( 28- 0)2 /12 = 65.33 milli seconds 2

(c) E[A] = E[9X] = 9 *  21 = 189 milli seconds

(d) Var(A) = Var [ 9X] = 9 *  Var[X] = 9 * 65.33 = 588 ms2

std. dev. = 24.25 ms

(e) P( A> 216) = 1 - P(A < 216)

Z - value = ( 216 - 189) /24.25 = 1.1134

P - value from Z - table = 0.8438

so  P( A> 216) = 1 - P(A < 216) = 1 - 0.8438 = 0.1562

(f) P( A < 168) =?

Z vaalue = ( 168 - 189) / 24.25 = - 0.866 respective p value = 0.193

so P( A< 168) = 0.193

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