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    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: 126
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!
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    (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: 126
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.
 
 
 
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