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Advay Mansingka
Advay Mansingka
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Drawing Draw two numbers, A and B, from a set of integers {1, 2, 3, 4, 5, 6}. A and B are drawn sequentially without replacement. Find the variance Var(3A+B).

You draw two numbers, $A$ and $B$ from a set of integers $\{1,2,3,4,5,6\}$. The numbers are drawn sequentially from the set, without replacement. Find the variance $Var(3A+B)$.

I have tried working on this question for a bit but cannot seem to find a quick way to compute it - perhaps there is some insight that would allow us to skip a lot of the computation?. I do not have a lot of experience with similar questions and so I have just been trying a brute force approach so far. This quickly gets quite convoluted for me, as expanding to $Var(3A+B) = Var(3A) + Var(B) + Cov(3A,B)$ all require further sub steps. Any help greatly appreciated!

My approach so far

Drawing two numbers, A and B, from a set of integers {1, 2, 3, 4, 5, 6}. A and B are drawn sequentially without replacement. Find Var(3A+B).

I have tried working on this question for a bit but cannot seem to find a quick way to compute it - perhaps there is some insight that would allow us to skip a lot of the computation?. I do not have a lot of experience with similar questions and so I have just been trying a brute force approach so far. This quickly gets quite convoluted for me, as expanding to $Var(3A+B) = Var(3A) + Var(B) + Cov(3A,B)$ all require further sub steps. Any help greatly appreciated!

My approach so far

Draw two numbers, A and B, from a set {1, 2, 3, 4, 5, 6}. A and B are drawn sequentially without replacement. Find the variance Var(3A+B).

You draw two numbers, $A$ and $B$ from a set of integers $\{1,2,3,4,5,6\}$. The numbers are drawn sequentially from the set, without replacement. Find the variance $Var(3A+B)$.

I have tried working on this question for a bit but cannot seem to find a quick way to compute it - perhaps there is some insight that would allow us to skip a lot of the computation?. I do not have a lot of experience with similar questions and so I have just been trying a brute force approach so far. This quickly gets quite convoluted for me, as expanding to $Var(3A+B) = Var(3A) + Var(B) + Cov(3A,B)$ all require further sub steps. Any help greatly appreciated!

My approach so far

Source Link
Advay Mansingka
Advay Mansingka
  • 33
  • 6

Drawing two numbers, A and B, from a set of integers {1, 2, 3, 4, 5, 6}. A and B are drawn sequentially without replacement. Find Var(3A+B).

I have tried working on this question for a bit but cannot seem to find a quick way to compute it - perhaps there is some insight that would allow us to skip a lot of the computation?. I do not have a lot of experience with similar questions and so I have just been trying a brute force approach so far. This quickly gets quite convoluted for me, as expanding to $Var(3A+B) = Var(3A) + Var(B) + Cov(3A,B)$ all require further sub steps. Any help greatly appreciated!

My approach so far