AB20040301

# AB20040301 - 3-1

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Unformatted text preview: 3-1 古典機率論箱子內有編號為1號、2號、3號、…、48號、49號等共49個球，以抽取出來的球不再放回箱中的方式，從中隨機抽取6個球。(1) 求出現39號球的機率。(2) 求會出現29號但不出現39號球的機率。(3) 同時出現29號與39號球的機率。(4) 求全部出現奇數號球的機率。【世新資管】解(1)⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛64954811(2)⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛649547111(3)⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛6494471111(4)⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛64924625Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas casinos. A player is dealt two cards. Face card (jacks, queens, and kings) and tens have a point value of 10. Aces have a point value of 1 or 11. A 52-card deck has 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces. Now, a blackjack is a 10-point card and an ace for a value of 21. What is probability that a player is dealt blackjack? 【中原資管】解⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛2523211614From an ordinary deck of 52 cards, 4 cards are picked at random. Find the probability that (1) exactly one is an ace. (2) exactly one is a face card. (3) all are black cards. ☆☆☆類 題28☆☆☆類 題29★☆☆類 題304-1 隨機變數Find the values of the constant kthat define the following density functions for two discrete random variables and for one continuous random variable. (1) ykyf−=2)(, ∞=,,2,1Ly. (2) ykyfy−=2)(, ∞=,,2,1Ly. (3) )()(2yykyf−=, where 1≤<<≤βαyand >k【政大國貿】解(1) 1=k(2) 2ln1=k(3) )(2)(363322αβαβ−−−, 1≤<≤βαLet X be the number of accidents in a factory per week having the probability mass function )2)(1(1)(++=xxxf, L,2,1,=x. (1) Find the conditional probability )1X|4X(P≥≥. (2) Show that )(xfhas the properties of a pmf. 【清大資應】解(1) 52(2) 提示：131212112111)2)(1(1=+−+−=⎟⎠⎞⎜⎝⎛+−+=++∑∑∞=∞=LxxxxxxThe continuous r.v. X has d.f. F given by: ⎪⎪⎩⎪⎪⎨⎧>≤<⎟⎠⎞⎜⎝⎛−≤=2,12,312,)(F32xxxxcxx(1) Determine the constant c. (2) Determine the corresponding p.d.f. (3) Calculate the probability )1X(P<. 【淡江統計】解(1) 83=c(2) ⎪⎩⎪⎨⎧<<−=o.w.,2,4323)(2Xxxxxf(3) 21★★★類 題83★★☆類 題84★☆☆類 題864-2 若有一個cumulative distribution function如下：⎪⎪⎪⎩⎪⎪⎪⎨⎧≥<≤−<≤<=23,1231,211,2,)(FXxxxxxxx(1) 試繪出其圖形； (2)求其pdf，並繪出圖形； (3)求⎟⎠⎞⎜⎝⎛≤21XP；(4) 求⎟⎠⎞⎜⎝⎛≥21XP； (5)求)25.1X5.(P<<； (6)求)25.1X(P=。解(1) 121)(FXx21x)(Xxf12x121(2) ⎪⎪⎪⎩⎪⎪⎪⎨⎧<≤<≤=otherwise,...
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AB20040301 - 3-1

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