# Download Adjustment Computations: Spatial Data Analysis by Charles D. Ghilani PDF By Charles D. Ghilani

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A residual is the difference between any individual measured quantity and the most probable value for that quantity. Residuals are the values that are used in adjustment computations since most probable values can be determined. The term error is frequently used when residual is meant, and although they are very similar and behave in the same manner, there is this theoretical distinction. 3) where νi is the residual in the i th observation, yi , and y is the most probable value for the unknown.

8), the mean value of nε 2 = n (μ − y)2 will tend to n times the variance of y since ε represents the deviation of the sample mean from the population mean. Thus nε2 → n(σ 2 /n), where σ 2 /n is the variance in y as n → ∞. The discussion above and Equation (m) results in n nσ 2 → (yi − y)2 + σ 2 (n) (yi − y)2 → (n − 1) σ 2 (o) i =1 Rearranging Equation (n) produces n i =1 Thus from Equation (o) and recognizing the left side of the equation as (n − 1) S 2 for a sample set of data, it follows that S2 = n i =1 (yi − y)2 → σ2 n −1 (p) In other words, for a large number of random samples, the value of − y)2 /(n − 1) tends to σ 2 .

Box B contains five balls, two red and three white. What is the probability that two red balls would be drawn if one ball is drawn randomly from each box? The total number of possible pairs is 4 × 5, or 20, since by drawing one ball from box A, any of the five balls in box B would complete the pair. Now, there are only two ways to draw two red balls. That is, box A’s red ball can be matched with either red ball from box B. Therefore, the probability of obtaining two red balls simultaneously is 2/20.