You are given an insertion-only stream, only consisting of (add, i) updates where i e {1,...,n}.There are m such updates. Suppose you want to sample a random insertion in the stream.For example, if the insertions formed the sequence (1,3, 5, 5, 7, 1, 5) with m = 7, then the goalis to output 1 with probability 2/7, 3 with probability 1/7, 5 with probability 3/7, and 7 withprobability 1/7.Consider the following algorithm that acts as follows on the t'th insertion. If t = 1, let X bethe first inserted element. For t > 1, with probability 1/t, let X be the tth inserted elementand with probability 1– 1/t, don't change X. At the end of the stream, return X.Show that X is indeed uniformly sampled from the m insertions.

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Answered: You are given an insertion-only stream,…

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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In python: Modifydef clipped_hist(df, clip_threshold = 1) to plot a Gaussian distribution on top of a normalized histogram.

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