jueves, 24 de enero de 2013

Extra points: Problem

In this time for this entry, will solve the problem 1.5.2 of the book Introduction to Information Theory and Data Compression.

The problem here:

2. In eight tosses of a fair coin, find the probability that heads will come up
(a) exactly three times;
(b) at least three times;
(c) at most three times.

Answers:

A)
To solve this part i used next formula:


Where:
  • "k" is the number of hits.
  • "n" is the number of trials.
  • "p" is the probability of success
now resolve:

and the result is: 0.875


B)
To solve this part i used next formula


Where:
  • "k" is the number of hits.
  • "n" is the number of trials.
  • "p" is the probability of succes
  • "u" is the exactly k succes (sigma)

now resolve:

=


=



and the result is: 2.2226

C)
To resolve this part i used the next formula:

 Where:
  • P is probability of the event,
  • C (n, k) are combinations of k elements from n elements a total
  • p is the probability of success and q = (1-p) the probability of failure
  • n number of times to repeat the individual case
  • k number of successes
now resolve:

and the result is:1/256




1 comentario:

  1. Lo de A está bien; "exactly three times" = distribución binomial.
    En B, "at least three times", podrías sumar las distribuciones binomiales para k = 3, 4, 5, 6, 7, 8. Mientras "C" sería at most three times 1 - suma de binomiales de 0, 1, 2 y 3 ;)
    Van 2 pts extra. Tu respuesta de B está muy obviamente equivocada; debería ser una probabiidad y está encima de uno ;)

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