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1980tw asked in 科學數學 · 1 decade ago

數學 統計error of estimate一題!!

S以某個速度走路,求是否可以知道他的error of estimate of time(錯誤估計時間)是小於0.5小時?

給了兩個條件:

1. Error of estimate ofdistance is + - 10(正負10)

2. Error of estimate ofspeed is + - 5(正負5)

ANS:僅這兩個條件無法知道error of estimate of time是否小於0.5

(不確定是否正確...)

問題:

想請教是否有人清楚 error of estimate 之意思呢?是不是表示統計說的標準差誤差? 即是平均值加減一個標準差呢?

還有這題給定這兩個條件為什麼無法算出呢?該怎麼列算式呢?

感謝!!!

1 Answer

Rating
  • 1 decade ago
    Favorite Answer

    Error of estimate 就是指估計的誤差,跟你所指的標準差(standard deviation) 或標準誤差(standard error)都沒有關係。

    已知兩個條件:

    1. Error of estimate of distance is + - 10(正負10) (s)

    2. Error of estimate of speed is + - 5(正負5) (u)

    所需時間 t=s/u

    只有這兩個條件並不能知道估計所需時間的誤差有多大,舉個例子好了:

    假設 s = 100±10 km , u= 25±5 km/h

    所需時間 t 的真值: t = 100/25 = 4

    如果s和d的絕對誤差都在最大值時,t* = 110/20 = 5.5

    估計所需時間的絕對誤差=| t - t* | = 1.5 > 0.5

    所以要知道估計所需時間的誤差有多大,必須知道s跟u的估計值以及其絕對誤差才可以。

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