Question: An amplifier circuit has power consumption Y that grows nonlinearly with the input signal voltage X. When the input signal is X volts, the instantaneous

An amplifier circuit has power consumption Y that grows nonlinearly with the input signal voltage X. When the input signal is X volts, the instantaneous power consumed by the amplifier is Y = 20 + 15X2 Watts. The input signal X is the continuous uniform (-1,1) random variable. Sampling the input signal every millisecond over a 100-millisecond interval yields the iid signal samples X1, X2, ˆ™ ˆ™ ˆ™, X100- Over the 100 ms interval, you estimate the average power of the amplifier as

Where Yi = 20 +15X2i. Use the central limit theorem to estimate P[W ‰¤ 25.4].

100 i-1

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