8.5-bo'lim: Ehtimollik

1. Mayli, \[f\left( x \right) = \left\{ {\begin{array}{ll}{\displaystyle \frac{3}{{37760}}{x^2}\left( {20 - x} \right)}&{{\mbox{if }}2 \le x \le 18}\\0&{{\mbox{otherwise}}}\end{array}} \right.\]
   1. \(f\left( x \right)\) ehtimollik zichligi funksiyasi ekanligini ko'rsating.
   2. \(P\left( {X \le 7} \right)\) ni toping.
   3. \(P\left( {X \ge 7} \right)\) ni toping.
   4. \(P\left( {3 \le X \le 14} \right)\) ni toping.
   5. \(X\) ning o'rtacha qiymatini aniqlang.
   Yechim
2. Lampochka markasi uchun lampochkaning ishlash muddatining ehtimollik zichligi funktsiyasi quyidagi funktsiya bilan berilgan, bu erda t oylarda. \[f\left( t \right) = \left\{ {\begin{array}{ll}{0.04{{\bf{e}}^{ - \,\,\frac{t}{{25}}}}}&{{\mbox{if }}t \ge 0}\\0&{{\mbox{if }}t < 0}\end{array}} \right.\]
   1. \(f\left( t \right)\) ehtimollik zichligi funksiyasi ekanligini tekshiring.
   2. Lampochkaning ishlash muddati 8 oydan kam bo'lishi ehtimoli qanday?
   3. Lampochkaning 20 oydan ortiq xizmat qilish ehtimoli qanday?
   4. Lampochkaning 14 oydan 30 oygacha xizmat qilish ehtimoli qanday?
   5. Lampochkalarning ishlash muddatining o'rtacha qiymatini aniqlang.
   Yechim
3. \(c\) qiymatini aniqlang, buning uchun quyidagi funktsiya ehtimollik zichligi funktsiyasi bo'ladi. \[f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}{c\left( {8{x^3} - {x^4}} \right)}&{{\mbox{if }}0 \le x \le 8}\\0&{{\mbox{otherwise}}}\end{array}} \right.\] Yechim