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MMLU-Pro / 11955 / Consider a carrier m(t) = n(t) …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Consider a carrier m(t) = n(t) \bulletcos(\omega_ot+ \texttheta), amplitude modulated by the noise n(t), where \texttheta is a random variable with a probability density f(\texttheta) = {1 / 2\pi}- \pi \leq \texttheta \leq \pi and = 0elsewhere. If E[n^2(t)] = \sigma^2 and \texttheta and n(t) are independent, determine the power dissipated by m(t).

category

engineering

options

  1. (1/3)σ^2
  2. σ^2/π
  3. σ^4
  4. πσ^2
  5. (1/4)σ^2
  6. 2σ^2
  7. (3/4)σ^2
  8. (2/3)σ^2
  9. (1/2)σ^2
  10. σ^2

src

stemez-ElectronicCommunications

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Source and history

upstream_id / Original problem ID
11955
task_id
c9ca4157-ca96-5d1b-b56d-9dc0febb49fe
task_key
default--test--11955
task_revision_id
1
config / split
default / test

Official source

initial import