Question

Consider n independent trials, each of which results in one of the outcomes 1,..., k with respective probabilities p_1, ..., p_k, ?_{i=1}^k p_i = 1. Show that if all the pi are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) ?_i p_i^2 / 2)

Name: Consider n independent trials, each of which results in one of the outcomes 1,..., k with respective probabilities p1, ..., pk, ?i=1^k pi = 1. Show that if all the pi are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) ?i pi^2 / 2)
Uploaded: 2022-11-06T17:17:44-08:00
Duration: 4 min 17 s
Channel: Adi S
Description: Consider n independent trials, each of which results in one of the outcomes 1,..., k with respective probabilities p1, ..., pk, ?i=1^k pi = 1. Show that if all the pi are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) ?i pi^2 / 2)

          Consider n independent trials, each of which results in one of the outcomes 1,..., k with respective probabilities p_1, ..., p_k, ?_{i=1}^k p_i = 1. Show that if all the pi are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) ?_i p_i^2 / 2)

Consider n independent trials, each of which results in one of the outcomes 1,..., k with respective probabilities p1, ..., pk, ?i=1^k pi = 1. Show that if all the pi are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) ?i pi^2 / 2)

Added by Salvador J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

11/06/2022

Step 1

The probability that no trial outcome occurs more than once can be calculated by looking at the pairs of trials and finding the probability that each pair has the same outcome. ** Show more…

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Consider n independent trials, each of which results in one of the outcomes 1,..., k with respective probabilities p1, ..., pk, ∑ pi = 1. Show that if all the pi are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) ∑ pi^2 / 2).