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sharpruin

新虫 (初入文坛)

[求助] 求助数学高手

x={xi|xi∈[A,B]} , y={yi|yi∈[A,B]}, x~N(μx,δx), y~N(μy,δy), 求P(x<=y).其中xi 和yi 中 i 是下标,μx和μy中x 和y 也是下标,δx和δy中 x 和
y 也是下标,求高手求解。给出求解过程,给点思路也好,错了也没事,必有重谢。
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lllgold

银虫 (初入文坛)

【答案】应助回帖

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sharpruin: 金币+40, 博学EPI+1, ★有帮助 2014-07-16 13:45:00
??x={xi|xi??[A,B]} , y={yi|yi??[A,B]}
??x-y={xi-yi|xi-yi??[A-B,B-A]}????A-B??x-y??B-A
??x~N(??x,??x), y~N(??y,??y)
??x-y~N(??x-??y,??x+??y)
??[??x-y??-????x-??y??]/ sqr????x+??y??~N(0,1)
???A-B??x-y??B-A,??A-B??0??B-A
??P??x??y??=P??x-y??0??
         =P(A-B??x-y??0)
              =P?x[??A-B??-????x-??y??]/ sqr????x+??y) ?? [??x-y??-????x-??y??]/ sqr????x+??y??[0-????x-??y??]/ sqr????x+??y???y
         =???v[0-????x-??y??]/ sqr????x+??y???w?????v[??A-B??-????x-??y??]/ sqr????x+??y)?w
         =???v??-??x+??y??/ sqr????x+??y???w?????v[??A-B??-????x-??y??]/ sqr????x+??y)?w?????????????????
???????????????????????????????????????????,??????????????????????
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2楼2014-06-30 10:19:12
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lllgold

银虫 (初入文坛)

【答案】应助回帖

对了,在以上答案中,写根号时不方便,用“sqr”代替了根号。
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3楼2014-06-30 10:27:25
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