Exercise 2.18 Compute the average number of fixed points in the set of permutations of n elements. The average number of fixed points is the ratio between the total number of fixed points in all the permutations and the number of permutations.
Added by Jessica M.
Close
Step 1
A fixed point in a permutation is an element that remains in its original position. In a permutation of n elements, there can be at most n fixed points (if the permutation is the identity permutation). To find the total number of fixed points in all Show more…
Show all steps
Your feedback will help us improve your experience
Marc Lauzon and 100 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let G be the set of all permutations of the set { 1, 2, . . . , n }, and let n be an integer ≥ 2. For each σ ∈ G, let X(σ) be the number of inversions for σ, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n such that σ(i) > σ(j). Calculate the average value of X:
Madhur L.
Dr. C D.
Let D(n) be the number of derangements in [n] (recall that these are permutations without fixed points). Give a combinatorial proof of the formula D(n + 1) = n(D(n) + D(n - 1)).
Adi S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD