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Old 05-05-2018, 03:24 AM
fjmvasa fjmvasa is offline
Join Date: Apr 2018
Posts: 7
Smile Darth Vader Rule Question

Hi everyone! I would like to ask if the Darth Vader also applies for x < 0? Since there is a rule for a < x < infinity.
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Old 05-05-2018, 04:35 AM
Michael Mastroianni's Avatar
Michael Mastroianni Michael Mastroianni is offline
Join Date: Jan 2018
Posts: 33

If is a random variable defined on and then is defined on right? So is nonnegative and you can use the rule:

Where the last part uses substitution:

But also from linearity we know

Add to both sides for:

So in this limited case it does extend to negative values. I hope that helps.
Michael Mastroianni, ASA
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Old 05-06-2018, 11:03 PM
fjmvasa fjmvasa is offline
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Thank you very much Michael!
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