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polu asked in 教育與參考考試 · 1 decade ago


若棒球名投手王建民去年投球紀錄為投出直球、下墜球與上飄球之比率為 28:34:38。

今欲觀測其未來投出10 球中,直球、下墜球與上飄球之球數,則:

請定義必要之隨機變數並列出其衍生的樣本空間(induced sample space)。

請推導(Derive)其機率函數(probability function),並敘明該機率模式之名稱。

請問其恰投出2 次直球、3 次下墜球與5 次上飄球之機率為何?

請問其投出直球之期望數(expected number)與變異數(variance)為何?

若已知投手王建民投出直球、下墜球與上飄球為好球之機率分為0.88, 0.82 與0.8,則請問其投出好球之機率為何?


1 Answer

  • 1 decade ago
    Favorite Answer

    這是基本的Multinomial Distribution直球、下墜球與上飄球之球數: X1,X2,X3P(X1=x1,X2=x2,X3=x3)=[10!/(x1!*x2!*x3!)]*[0.28^x1]*[0.34^x2]*[0.38^x3]其恰投出2 次直球、3 次下墜球與5 次上飄球之機率:P(X1=2,X2=3,X3=5)其投出直球之期望數(expected number)與變異數(variance):10*0.28,10*0.28*0.72若已知投手王建民投出直球、下墜球與上飄球為好球之機率分為0.88, 0.82 與0.8,則請問其投出好球之機率為何?0.28*0.88+0.34*0.82+0.38*0.8

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