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Thread: Showing that X1+X2=2X1 for random variable X1, X2 such that X1=X2

  1. #1
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    Showing that X1+X2=2X1 for random variable X1, X2 such that X1=X2

    I need help understanding this problem.

    Say that X1=X2 which means that the random variable X1 and X2 are equal in distribution. This means that these two random variables have the same distribution, same mean and same variance. These two random variables are independent. Is it true that X1+X2=2X1?

    In my head this makes perfect sense but i am having trouble writing a proof to this.

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    Quote Originally Posted by ajorge View Post
    I need help understanding this problem.

    Say that X1=X2 which means that the random variable X1 and X2 are equal in distribution. This means that these two random variables have the same distribution, same mean and same variance. These two random variables are independent. Is it true that X1+X2=2X1?

    In my head this makes perfect sense but i am having trouble writing a proof to this.
    Just Mean and Variance?

    Do you mean IDENTICAL, or just the first two moments?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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    Quote Originally Posted by tkhunny View Post
    Just Mean and Variance?

    Do you mean IDENTICAL, or just the first two moments?
    From my understanding the question only has those two moments and they are identical.

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    From my understanding those are two moments that are Identical

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    Quote Originally Posted by ajorge View Post
    From my understanding those are two moments that are Identical

    Can you write out the definition of E[X1]? That should get you started.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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