Nneetquant

Summing normals

EasyRandom VariablesStatistics~2m

X∼N(1, 4)X\sim N(1,\,4) and Y∼N(2, 9)Y\sim N(2,\,9) are independent (variances 44 and 99). What is the variance of X+YX+Y?

Show hints (2)+
  1. A sum of independent normals is normal.
  2. Independent variables add variances: 4 + 9.

Answer

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13

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Asked at: Optiver, IMC

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