Question

A four-sided fair die is rolled twice. Let X be the number comes up at the first roll and Y be a random variable taking a value of 1 if the numbers on the first and second rolls are the same, otherwise it takes a value of 0. a) Find the joint probability distribution of X and Y . b) Calculate cov(X, Y ). c) Determine whether X and Y are independent or not. 

          A four-sided fair die is rolled twice. Let X be the number comes
up at the first roll and Y be a random variable taking a value of 1
if the numbers on the first and second rolls are the same,
otherwise it takes a value of 0.
a) Find the joint probability distribution of X and Y .
b) Calculate cov(X, Y ).
c) Determine whether X and Y are independent or not.
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A four-sided fair die is rolled twice. Let X be the number comes up at the first roll and Y be a random variable taking a value of 1 if the numbers on the first and second rolls are the same, otherwise it takes a value of 0. a) Find the joint probability distribution of X and Y . b) Calculate cov(X, Y ). c) Determine whether X and Y are independent or not.
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Transcript

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00:01 Hello in the following question first of all we made the sample space so the sample space is which is equals to one one two one three one four then two one two two three two four then three one three three four then four one four two four two four two four two four two four two 4 3 and 4 4 4 so now we will get x has 4 values 1 2 3 4 and y has 2 values…
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