GATE CE 2015 Set 1 — Question 64
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Geomatics Engineering → Errors & Adjustment → Error Propagation
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Question
In a survey work, three independent angles , and were observed with weights , , , respectively. The weight of the sum of angles , and is given by:
Correct answer
(A) 1 / ((1)/(W_X) + (1)/(W_Y) + (1)/(W_Z))
Solution
The weight of a sum of independent observations is equal to the reciprocal of the sum of the reciprocals of the individual weights. If , then the variance of the sum is the sum of the variances: . Since weight is inversely proportional to variance (), we have . Solving for gives .
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