The function β(q) is determined by the equation |
(p1q)(r1β(q)) + ...
+ (pNq)(rNβ(q)) = 1 (*) |
Recall that 0 < ri < 1 and 0 < pi < 1 for all i. |
As q → ∞, each piq → 0,
and so at least one of the riβ(q) must become arbitrarily
large if equation (*) is to hold. |
In order for any of the riβ(q) to become arbitrarily
large, we must have β(q) → -∞. |
  |
As q → -∞, each piq → ∞,
and so each riβ(q) must go to 0 if equation (*) is to hold. |
In order for riβ(q) → 0, we must have
β(q) → ∞. |
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