Statistics-expectations

Could someone please explain to me the impact modulus signs have on expectation. E.g E(|X-Y|). I need to apply this to some questions but was not taught about it so any guidance would be appreciated. Also, how would you calculate the expectation of the product of RVs e.g E((x y)|x-y|). I can't find much about this online
Thank you

(edited 5 years ago)

OP

Anyone?

Original post by MissMathsxo

Could someone please explain to me the impact modulus signs have on expectation. E.g E(|X-Y|). I need to apply this to some questions but was not taught about it so any guidance would be appreciated. Also, how would you calculate the expectation of the product of RVs e.g E((x y)|x-y|). I can't find much about this online
Thank you

Imagine you had a random variable X on [-10,10] with a uniform distribution, then
E(x) = 0
but
E(|x|) = 5
Easy to spot as you fold the distribution for |x| would be uniform on [0,10]. Note
E(x^2)
is part of the variance expression. The x^2 transforms the original random variable and makes it non-negative. Its sometimes proposed as a robust (median) estimator.

It would probably be easier to post a question you're not sure about to give more direct help?

Reply 3

Gregorius

14

Original post by MissMathsxo

Also, how would you calculate the expectation of the product of RVs e.g E((x y)|x-y|). I can't find much about this online
Thank you

If X and Y are independent random variables, then the expectation of their product is the product of their expectation; if not, you need the idea of Covariance.

Statistics-expectations

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