Hey there! Sign in to join this conversationNew here? Join for free

Joint Probability Watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    I am working on the following question:We choose numbers from {2; 3} by tossing a fair coin; the coin is tossed twice. Choose 2 if the coin turns up Heads and 3 if the coin is Tails. So the possible outcomes are {(2, 2), (2, 3), (3, 2), (3, 3)}. Let X be the first number chosen (so X is an element of {2, 3}) and let Y be the product of the two chosen numbers. Write down the joint distribution of X and Y as a table.My solution so far:This is my table for the joint probability:Name:  1.png
Views: 113
Size:  5.2 KBTable for probability of Y:Attachment 499007499009499000Table for probability of X:Attachment 499007499009499000


    However there is a problem with the table for the probability of X. So I obtain the probabiity for each X = a by summing the rows in the joint probability table. But when I count the sample space it is different. In the cell (1,1) we have 1/4 but that cannot be right, it should be 1/2 because there are 2 events in the sample space that have the number 2 on first flip.

    What is wrong?!

    edit: something seems to be wrong uploaded the images for the last two tables. Click on the attachments!
    Attached Images
      
    • Very Important Poster
    • Welcome Squad
    Offline

    20
    ReputationRep:
    (Original post by aspiring_doge)
    I am working on the following question:We choose numbers from {2; 3} by tossing a fair coin; the coin is tossed twice. Choose 2 if the coin turns up Heads and 3 if the coin is Tails. So the possible outcomes are {(2, 2), (2, 3), (3, 2), (3, 3)}. Let X be the first number chosen (so X is an element of {2, 3}) and let Y be the product of the two chosen numbers. Write down the joint distribution of X and Y as a table.My solution so far:This is my table for the joint probability:Name:  1.png
Views: 113
Size:  5.2 KBTable for probability of Y:Attachment 499007499009499000Table for probability of X:Attachment 499007499009499000


    However there is a problem with the table for the probability of X. So I obtain the probabiity for each X = a by summing the rows in the joint probability table. But when I count the sample space it is different. In the cell (1,1) we have 1/4 but that cannot be right, it should be 1/2 because there are 2 events in the sample space that have the number 2 on first flip.

    What is wrong?!

    edit: something seems to be wrong uploaded the images for the last two tables. Click on the attachments!
    I'm not sure why you think that the probability for getting 2 on the first turn is 25%, it's 50% your table of outcomes is correct though. Just not your table for X values.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Break up or unrequited love?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.