Two fair dice are rolled. Let X be the difference between the numbers showing on the two dice. Find its pdf pX.? collage statistics , can u please show work
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Well, think about your sample space. there are 6^2=36 possible combinations of rolls (some have the same numbers showing).
The possible outcomes (the difference between the numbers showing on the dice) are 0, 1, 2, 3, 4, 5.
So you need to figure out the probability for each of the 6 outcomes, which is the number of ways that outcome can occur / 36
E.g. for X=0 you have the following rolls:
So P(0)=6/36 = 1/6
Now consider the possibilities for each of the other values for X, 1 - 5.
So P(1)=10/36 = 5/18
Remember, when you have done all the possible outcomes, the probabilities should sum to 1.
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so up to how money time
no i mean to do the sum do i have to to next steps is with 2 then 3, 4, 5, 6 or just stop in 5th
Your random variable X is "the difference between the numbers showing on the two dice". You can't roll 2 dice and have a difference of 6 (since you cant roll anything less than 1 or higher than 6). So you need to find the probabilities for 0, 1, 3, 4, and 5. I did the first two for you.