a permutation on a list of numbers 1 n is a function defined from 1 n to 1 n where i yields the

Name: a permutation on a list of numbers 1 n is a function defined from 1 n to 1 n where i yields the position of i in the permutation a fixed point of a permutation is a value for which x x for a 93345
Uploaded: 2023-08-09T03:13:13-08:00
Duration: 3 min 6 s
Channel: Madhur L
Description: a permutation on a list of numbers 1 n is a function defined from 1 n to 1 n where i yields the position of i in the permutation a fixed point of a permutation is a value for which x x for a 93345

First, we need to find the total number of permutations for a list of n numbers. This is given b

Question

A permutation on a list of numbers [1, ..., n] is a function π defined from [1, ..., n] to [1, ..., n], where π(i) yields the position of i in the permutation π. A fixed point of a permutation π is a value for which π(x) = x. For a given permutation π, what will be the expected number of fixed points?

          A permutation on a list of numbers [1, ..., n] is a
function π defined from
[1, ..., n] to [1, ..., n], where
π(i) yields the position of i in the
permutation π. A fixed
point of a permutation π is a
value for which π(x) =
x. For a given
permutation π, what will be
the expected number of fixed points?

Added by Michelle P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/09/2023

Step 1

This is given by n! (n factorial). Now, let's define an indicator variable I_i for each position i in the permutation, where I_i = 1 if π(i) = i (i.e., i is a fixed point) and I_i = 0 otherwise. The total number of fixed points in a permutation π is the sum of Show more…

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A permutation on a list of numbers [1, ..., n] is a function π defined from [1, ..., n] to [1, ..., n], where π(i) yields the position of i in the permutation π. A fixed point of a permutation π is a value for which π(x) = x. For a given permutation π, what will be the expected number of fixed points?