AB20040301 - 3-1

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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,...
View Full Document

{[ snackBarMessage ]}

Page1 / 93

AB20040301 - 3-1

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online