I need explination in details how did we calculate it   The Shannon Game intuition for perplexity - Josh Goodman: imagine a call-routing phone system gets120 Kcalls and has to recognize - "Operator" (let's say this occurs 1 in 4 calls) - "Sales" (1in 4) - "Technical Support" (1 in 4) - 30,000 different names (each name occurring 1 time in the 120K calls) We get the perplexity of this sequence of length120Kbyfirst multiplying120 Kprobabilities (90K of which are1/4and30 Kof which are1/120 K), nd then taking the inverse 120,000 th root: \[ \text { Perp }=\left(1 / 4 * 1 / 4 * 1 / 4 * 1 / 4 * 1 / 4 * \ldots .{ }^{*} 1 / 120 \mathrm{~K} * 1 / 120 \mathrm{~K} * \ldots .\right)^{\wedge}(-1 / 120 \mathrm{~K}) \] But this can be arithmetically simplified to justN=4: the operator(1/4), the sales(1/4), the tech support(1/4), and the 30,000 names(1/120,000): Perplexity=((1/4∗1/4∗1/4∗1/120 K)∧(−1/4)=52.6

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