kirbykirby
  • kirbykirby
If \(X_i\),\(Y_j\) are random variables, and \(a_i\), \(c_j\), \(b\), \(d\) \(\in \mathbb{R}\), \(i=1,2,...,n\); \(j=1,2,...,m\), then show that \[Cov \left( \sum_{i=1}^{n}a_i X_i+b,\sum_{j=1}^{m}c_j Y_j+d \right) =\sum_{i=1}^{n}\sum_{j=1}^{m}a_i c_j Cov(X_i,Y_j)\] Is there a way to do this without induction? I started doing it that way, but the algebra is extremeeely messy.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
proof that the covariance is equal to that other stuff eh
amistre64
  • amistre64
im thinking an "easier" route might be to consider the algebra involved
amistre64
  • amistre64
define the formula for covariance, input the given parts, and reduce it to the right side ....

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kirbykirby
  • kirbykirby
oh i see what you mean. I suppose that wold involve less algebra than induction, though still a bit messy I suppose. :)

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