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Exercise 2.4.1

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Take derivative of $V - λ (p_{1} + \dots + p_{n} - 1)$ w.r.t. $p_{i}$ , we have $\frac{∂V}{\partial p_{i}} = - \frac{a_{i}^{2}}{p_{i}^{2}} - λ = 0$ , we have $p_{i} = \frac{a_{i}}{\sqrt{- λ}}$ , use the condition that $p_{1} + \dots + p_{n} = 1$ , we have $λ = - {(\sum a_{i})}^{2}$ , $p_{i} = \frac{a_{i}}{\sum a_{i}}$

niuers

2020-03-20 00:00

Exercise 2.4.1

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