1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability mass function

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppose we roll a fair die. Whatever number comes up, we toss a coin that many times. What is the probability mass function of the number of heads?


    2. Relevant equations
    N/A


    3. The attempt at a solution
    Let X=number of heads
    Then I know that X can take on the values 0,1,2,3,4,5,6.
    How to proceed from here I have no clue...


    Could someone please explain? Any help would be appreciated!
     
  2. jcsd
  3. Oct 30, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Just direct computation. The probability of 0 is 0 because there is no "0" on a die. What is the probability of rolling a 1 on a die? Of a 2? etc.
     
  4. Oct 30, 2008 #3
    By the way, is this a "birvariate" distirbution? How can I define the other random variable?
     
  5. Oct 31, 2008 #4
    Could somebody please help? I am totally stuck...
     
  6. Oct 31, 2008 #5

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Start with the probability of rolling a one....what is that?
     
  7. Oct 31, 2008 #6

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Literally, see what the probability of getting 1 heads is by finding the probability you roll x on the die, and multiplying by the probability of getting 1 heads in x coin flips. Rinse and repeat
     
  8. Oct 31, 2008 #7
    Uniform prob. of 1/6 for each number on the die
    And the prob. of a head is 1/2
    ...but I am still having trouble combining these...
     
  9. Oct 31, 2008 #8
    Probability of 6 heads= 1/6 times (1/2)^6

    Probabilty of 5 heads=.....(no, it's not just 1/6 times (1/2)^5)
     
  10. Nov 1, 2008 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Take it ones step at a time.

    There is a 1/6 probability of rolling a "1" and then you flip the coin once which has probability 1/2 of getting a head: probability of getting 1 head this way is (1/6)(1/2)= 1/12.

    There is a probability of 1/6 of rolling a 2 and then you flip the coin twice which has a probability 1/2 go getting one head and a probability 1/4 of getting two heads.
    Probability of getting 1 head this way is 1/12 and probability of getting two heads is 1/24.

    Do you see a pattern? If you roll an "n" on the coin you flip the coin n times. You have a probability of 1-(1/2)^n of getting a 1. Altogether the probability getting a one is (1/6)(1/2+ 1/4+ 1/8+ ...). What is the probability of getting two heads if you fllip a coin n times? What is the probability of rolling an "n"?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Probability mass function
Loading...