Suppose that a game is to be played with a single die assumed fair. In this game a player wins $20 if a 2 turns up; $40 if a 4 turns up: loses $30 if a 6 turns up; while the player neither wins nor loses if any other face turns up.Find the variance for the game

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Suppose that a game is to be played with a single die assumed fair. In this game a player wins $20 if a 2 turns up; $40 if a 4 turns up: loses $30 if a 6 turns up; while the player neither wins nor loses if any other face turns up.Find the variance for the game

 

الأجوبة

دالة الاحتمال كالتالي:

30- 0 40 0 20 0 x
1/6 1/6 1/6 1/6 1/6 1/6 f(x)

التوقع هو μ=5 وبالتالي فإن التباين نحصل عليه كالتالي:

σ_X^2=(0-5)^2 (1/6)+(20-5)^2 (1/6)+(0-5)^2 (1/6)+(40-5)^2 (1/6)+(0-5)^2 (1/6)+(-30-5)^2 (1/6)=2750/6=458.333

وبالتالي يمكن إيجاد الانحراف المعياري بإيجاد الجذر التربيعي للتباین:

σ_X=√458.333=21.40872096

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