H10:07••.o Define the cumulative sumsSi= a1 + a2+...+ ai andSo = 0.Pick a random integer r uniformlybetween 0 and Sn – 1.-o Find the unique index i between 1and n such that S;-1 (€)10:06••.1. Discrete distribution. Write aprogram DiscreteDistribution.javathat takes an integer command-lineargument m, followed by asequence of positive integercommand-line argumentsa1, a2,..random indices (separated bywhitespace), choosing each index iwith probability proportional to a¡.An, and prints m9 •• •-/Desktop/arrays> java DiscreteDistribution 25 1 1 1 1115 2 4 4 5 5 4 3 4 3 1 5 2 4 2 6 1 3 6 2 3 2 4 1 4~ /Desktop/arrays> java DiscreteDistribution 25 10 10 10 10 10 503 6 6 16 6 2 4 6 6 3 6 6 6 6 4 5 6 2 2 66 2 6 2-/Desktop/arrays> java DiscreteDistribution 25 80 201 2 1 2 1 1 2 1 1 1 1 1 1 11 2 2 2 1 111111~/Desktop/arrays> java DiscreteDistribution 100 301 176 125 97 79 67 58 51 466 2 4 3 2 3 3 1 7 1 1 3 47 1 4 2 2 1 1 3 1 8 6 21 3 6 185 1 3 6 1 1 2 3 8 7 4 6 4 3 1 5 3 3 7 31 3 177 2 2 3 6 5 4 1 1 1 7 2 3 5 2 2 1 4 1 2 12 1 2 2 3 2 8 4 3 2 1 8 3 5 3 3 8 1 2 3 3 1 2 3 1To generate a random index i withprobability proportional to a;:o Define the cumulative sumsS; =a1 + a2 +...+ a; and0.SoPick a random integer r uniformlybetween 0 and Sn – 1.o Find the unique index i between 1and n such that S;-1 < r < S¿.-Geometrically, this subdivides theinterval [0, Sn) into n subintervals[S;-1, S;), with the length ofsubinterval i proportional to aj. Forexample, if the discrete distributionis defined hy.

public class DiscreteDistribution { public static void main(String[] args) { // read in…

Discrete distribution. Write a program DiscreteDistribution.java that takes an integer command-line argument m, followed by a sequence of positive integer command-line arguments A1, a2, . .., An, and prints m random indices (separated by whitespace), choosing each index i with probability proportional to a¡.

Discrete distribution. Write a program DiscreteDistribution.java that takes an integer command-line argument m, followed by a sequence of positive integer command-line arguments A1, a2, . .., An, and prints m random indices (separated by whitespace), choosing each index i with probability proportional to a¡.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

H
10:07
••.
o Define the cumulative sums
Si
= a1 + a2+...+ ai and
So = 0.
Pick a random integer r uniformly
between 0 and Sn – 1.
-
o Find the unique index i between 1
and n such that S;-1 <r < S;.
Geometrically, this subdivides the
interval [0, Sn) into n subintervals
[S;-1, S;), with the length of
subinterval i proportional to a¡. For
example, if the discrete distribution
is defined by
(а1, а2, аз, а4, аs , а6) — (10, 10, 10, 10, 1
then the cumulative sums are
(S1, S2, S3, S4, S5, S6) = (10, 20, 30, 40,
and the following diagram
illustrates the 6 subintervals:
Pick a random integer r between 0 and S, - 1.
1 if 0sr< 10
4 if 30 sr< 40
6 if 50 sr< 100
10
20
30
40
50
100
So
S2
S3
Ss
S6
In probability theory, this is known
as sampling from a discrete
distribution.

(€)
10:06
••.
1. Discrete distribution. Write a
program DiscreteDistribution.java
that takes an integer command-line
argument m, followed by a
sequence of positive integer
command-line arguments
a1, a2,..
random indices (separated by
whitespace), choosing each index i
with probability proportional to a¡.
An, and prints m
9 •• •
-/Desktop/arrays> java DiscreteDistribution 25 1 1 1 111
5 2 4 4 5 5 4 3 4 3 1 5 2 4 2 6 1 3 6 2 3 2 4 1 4
~ /Desktop/arrays> java DiscreteDistribution 25 10 10 10 10 10 50
3 6 6 16 6 2 4 6 6 3 6 6 6 6 4 5 6 2 2 66 2 6 2
-/Desktop/arrays> java DiscreteDistribution 25 80 20
1 2 1 2 1 1 2 1 1 1 1 1 1 11 2 2 2 1 111111
~/Desktop/arrays> java DiscreteDistribution 100 301 176 125 97 79 67 58 51 46
6 2 4 3 2 3 3 1 7 1 1 3 47 1 4 2 2 1 1 3 1 8 6 2
1 3 6 185 1 3 6 1 1 2 3 8 7 4 6 4 3 1 5 3 3 7 3
1 3 177 2 2 3 6 5 4 1 1 1 7 2 3 5 2 2 1 4 1 2 1
2 1 2 2 3 2 8 4 3 2 1 8 3 5 3 3 8 1 2 3 3 1 2 3 1
To generate a random index i with
probability proportional to a;:
o Define the cumulative sums
S; =
a1 + a2 +...+ a; and
0.
So
Pick a random integer r uniformly
between 0 and Sn – 1.
o Find the unique index i between 1
and n such that S;-1 < r < S¿.
-
Geometrically, this subdivides the
interval [0, Sn) into n subintervals
[S;-1, S;), with the length of
subinterval i proportional to aj. For
example, if the discrete distribution
is defined hy.

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