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Alexandre Eremenko
Alexandre Eremenko
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This is called the Darmois-Skitovich theorem. Of course, one needs to add the condition that $a_jb_j\neq 0$.

The reference is MR0346969 Kagan, A. M.; Linnik, Yu. V.; Rao, C. R., Characterization problems in mathematical statistics. Translated from the Russian by B. Ramachandran. John Wiley & Sons, New York-London-Sydney, 1973.

This is called the Darmois-Skitovich theorem. The reference is MR0346969 Kagan, A. M.; Linnik, Yu. V.; Rao, C. R., Characterization problems in mathematical statistics. Translated from the Russian by B. Ramachandran. John Wiley & Sons, New York-London-Sydney, 1973.

This is called the Darmois-Skitovich theorem. Of course, one needs to add the condition that $a_jb_j\neq 0$.

The reference is MR0346969 Kagan, A. M.; Linnik, Yu. V.; Rao, C. R., Characterization problems in mathematical statistics. Translated from the Russian by B. Ramachandran. John Wiley & Sons, New York-London-Sydney, 1973.

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Alexandre Eremenko
Alexandre Eremenko
  • 91.8k
  • 9
  • 259
  • 429

This is called the Darmois-Skitovich theorem. The reference is MR0346969 Kagan, A. M.; Linnik, Yu. V.; Rao, C. R., Characterization problems in mathematical statistics. Translated from the Russian by B. Ramachandran. John Wiley & Sons, New York-London-Sydney, 1973.