PLEASE SHOW ALL WORK FOR NUMBER 1, 2, AND 3! Suppose a college has a master file

Question

PLEASE SHOW ALL WORK FOR NUMBER 1, 2, AND 3!

Suppose a college has a master file consisting of 8,000 student records. Suppose that a Hash table has been constructed to hold 24,000 records, and currently holds 8,000 records. A new student is added to the master file. What is the average number of probes required to insert a new record into the Hash table for this student? The distribution X to solve this problem is called a Geometric Distribution. The probability q that a probe will find an occupied row in the Hash table is Q = _____ 2. The solution to the problem is mu = ____The probability that it will take more than 2 probes to enter this new record is Pr (X > 2) = ________

Explanation / Answer

The total number of occupied places = 8000

so probability of gettin a space p^ = (24000 - 8000)/ 24000 = 2/3

1. So the probability that a probe will find an occupied row in the Hash tables is = 2/3

2. The PMF of X, where X is the average number of probes required to insert a new record into the hash table.

f(x) = (1-2/3)x-1 (2/3) = (1/3)x-1 (2/3)

so E(X) = 1/q = 1/(2/3) = 3/2

3. Probability that it will take more than 2 probes to enter this record = 1- [P(x=1) + P(x=2)]

= 1 - [ (1/3)0(2/3) + (1/3)1 (2/3)] = 1- [ 2/3 + 1/9] = 2/9

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