{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmlu-pro","formal_name":"MMLU-Pro","introduction":"MMLU-Pro rebuilds MMLU with ten answer options instead of four and removes items that no longer separate models. Questions span fourteen academic and professional subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"43e0d954-15ae-5d88-ac73-4432dc9a82a6","task_key":"default--test--11803","task_revision_id":"1","upstream_id":"11803","short_description":"The error due to thermal noise in a communication sys-tem is represented by a…","config":"default","split":"test","body":"{\"category\":\"engineering\",\"options\":\"['0.656 [{2^(2N+1)S^2P_eI^2} / {2 T_s}]', '0.756 [{2^(2N+1)S^2P_eI^2} / {3 T_s}]', '0.656 [{2^(2N)S^2P_eI^2} / {2 T_s}]', '0.856 [{2^(2N)S^2P_eI^2} / {2 T_s}]', '0.856 [{2^(2N-1)S^2P_eI^2} / {3 T_s}]', '0.856 [{2^(2N)S^2P_eI^2} / {3 T_s}]', '0.756 [{2^(2N)S^2P_eI^2} / {3 T_s}]', '0.756 [{2^(2N)S^2P_eI^2} / {2 T_s}]', '0.656 [{2^(2N)S^2P_eI^2} / {3 T_s}]', '0.656 [{2^(2N-1)S^2P_eI^2} / {3 T_s}]']\",\"question\":\"The error due to thermal noise in a communication sys-tem is represented by a pulse train of amplitude\\\\Deltam_S. Let P(t) = [(I\\\\Deltam_s) / (\\\\tau)] be the pulse slope,t\\\\varepsilon[0, \\\\tau] where \\\\tau = (1 / 2f_m), calculate the power spectral density of the thermal noise,G_th(f) and the output noise power due to thermal noise error, N_th. Assuming that the duration of each error pulse is when the transmitted signal is (1 / 2f_m) sampled at theNyquistrate. Given:(\\\\Deltam_s)^2 = [(2^2N-1) / (3n)] S^2 and T = (T_s /NP_e) is the Threshold equation \\\\cong [{1} / {(16)2^2N}].\",\"src\":\"stemez-ElectronicCommunications\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}