Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Expected Sequences in a Random Events

  1. Feb 22, 2010 #1
    How many heads in a row would you expect to find if you toss a fair coin 8 times?







    I am thinking that the probability of 3 heads is 1/8 and since you have 8 tosses, that would give an E(x) of 1. So I am guessing that 3 is the number of heads one would expect to see in a fair coin is tossed 8 times. But I am not sure... Any help?
     
  2. jcsd
  3. Feb 23, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    You can do this in two ways, the basic method and the shorter method.

    The basic way is to use the definition of E(X)= ∑all x x*P(X=x)

    Write out in a tabular form, the distribution

    x
    P(X=x)

    x is the number heads obtained, so x goes from 0 to 8.


    The other way is to see if the question can be fitted to a special type distribution.
     
  4. Feb 23, 2010 #3

    statdad

    User Avatar
    Homework Helper

    I need some clarification: which question is of interest:

    1) How many heads would you expect to occur during 8 flips of a fair coin?

    2) If a fair coin is flipped 8 times, how long a sequence of consecutive heads would you expect to occur? (I phrased this from your wording "How many heads in a row...")

    These questions are not the same.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook