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I am having some difficulty understanding the following formula (primarily because of presence of a summation symbol in the denominator)

$ A = \frac{ \sum_{i=0}^1 (x_i+1) \times P_i} {\sum_{i=0}^1 P_i} $

Here is my interpretation of what the formula means $A = \frac {((x_0+1)\times P_0)}{P_0} + \frac{((x_1+1)\times P_1)}{P_1} $

Am I getting this right ? Any suggestions would be appreciated

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Nope, what you have is incorrect. $$\dfrac{\sum_{i=0}^1 (x_i+1)P_i}{\sum_{i=0}^1 P_i} = \dfrac{(x_0+1)P_0 + (x_1 + 1)P_1}{P_0 + P_1}$$ The above is the correct interpretation. What you have written is $$\dfrac{((x_0+1)\times P_0)}{P_0} + \dfrac{((x_1+1)\times P_1)}{P_1}$$ which is $$\sum_{i=0}^1 \dfrac{(x_i+1)P_i}{P_i}$$

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  • $\begingroup$ Thanks for clearing that up $\endgroup$ – Rajeshwar Apr 22 '13 at 23:35
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No this is not right. You treat the numerator and the denominator independently. A is one fraction, not a sum of fractions as you have written. What you have written would be the case if it were $\sum_{i=0}^1 \frac{(x_i+1)P_i}{P_i}$.

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