If XYZ are rvs such that X and Y are independent and Y and Z

If X,Y,Z are r.v.s such that X and Y are independent and Y and Z are independent, does it follow that X and Z are independent?

Hint: Think about simple and extreme examples.

Can someone give me an example of when this would happen?

Solution

Answer to the question)

Yes when X and Y are independent and Y and Z are indepednent , mathematically it does imply that X and Z are also independent

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Suppose X = score of A in SAT

Y = socre of B in SAT

Z = score of C in SAT

Now since scores of A and B are independent , and scores of B and C are also independent

this also follows that scores of A and C are also independent