{"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":"d3a2e6de-40c2-5e9c-9f40-8878995d6bce","task_key":"default--test--12119","task_revision_id":"1","upstream_id":"12119","short_description":"A random variable R has a Rayleigh density f(r) = (r / \\alpha^2)e[{-(r)2} /…","config":"default","split":"test","body":"{\"category\":\"engineering\",\"options\":\"['E[R] = \\\\\\\\sqrt{\\\\\\\\pi}\\\\\\\\alpha/2, E[R^2] = \\\\\\\\pi\\\\\\\\alpha^2/2, \\\\\\\\sigma_r^2 = (\\\\\\\\pi - 3)\\\\\\\\alpha^2/2', 'E[R] = 2\\\\x07lpha^2, E[R^2] = [\\\\\\\\surd(\\\\\\\\pi / 2)] \\\\x08ullet \\\\x07lpha, \\\\\\\\sigma_r^2 = \\\\x07lpha^2(0.43)', 'E[R] = \\\\\\\\alpha(1 - e^{-1/2}), E[R^2] = \\\\\\\\alpha^2, \\\\\\\\sigma_r^2 = \\\\\\\\alpha^2(e - 2)', 'E[R] = \\\\x07lpha^2(0.43), E[R^2] = [\\\\\\\\surd(\\\\\\\\pi / 2)] \\\\x08ullet \\\\x07lpha, \\\\\\\\sigma_r^2 = 2\\\\x07lpha^2', 'E[R] = \\\\\\\\alpha\\\\\\\\sqrt{e}, E[R^2] = \\\\\\\\alpha^2\\\\\\\\ln(2), \\\\\\\\sigma_r^2 = \\\\\\\\alpha^2(2 - e/\\\\\\\\pi)', 'E[R] = [\\\\\\\\surd(\\\\\\\\pi / 2)] \\\\x08ullet \\\\x07lpha, E[R^2] = 2\\\\x07lpha^2, \\\\\\\\sigma_r^2 = \\\\x07lpha^2(0.43)', 'E[R] = [\\\\\\\\surd(\\\\\\\\pi / 2)] \\\\x08ullet \\\\x07lpha, E[R^2] = \\\\x07lpha^2(0.43), \\\\\\\\sigma_r^2 = 2\\\\x07lpha^2', 'E[R] = \\\\\\\\alpha^2, E[R^2] = (2/3)\\\\\\\\alpha^2, \\\\\\\\sigma_r^2 = (4 - \\\\\\\\pi)\\\\\\\\alpha^2/2', 'E[R] = \\\\\\\\alpha/\\\\\\\\sqrt{2}, E[R^2] = \\\\\\\\alpha^2, \\\\\\\\sigma_r^2 = \\\\\\\\alpha^2(\\\\\\\\pi - 2)/2', 'E[R] = \\\\\\\\alpha\\\\\\\\sqrt{2/\\\\\\\\pi}, E[R^2] = 3\\\\\\\\alpha^2/2, \\\\\\\\sigma_r^2 = \\\\\\\\alpha^2(1 - 2/\\\\\\\\pi)']\",\"question\":\"A random variable R has a Rayleigh density f(r) = (r / \\\\alpha^2)e[{-(r)2} / {2(\\\\alpha)2}],0 \\\\leq r \\\\leq \\\\infty and = 0,r < 0 Determine the following: (a) the expected value or R, E [R] (b) the expected value of R^2, E [R^2] and (c) the variance \\\\sigma^2 of R\",\"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":[]}