AB20040301 - 3-1 1234849496(1) 39(2) 2939(3) 2939(4)

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Unformatted text preview: 3-1 1234849496(1) 39(2) 2939(3) 2939(4) (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? 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. 28 29 304-1 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<<yand >k(1) 1=k(2) 2ln1=k(3) )(2)(363322, 1<Let 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. (1) 52(2) 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<. (1) 83=c(2) <<=o.w.,2,4323)(2Xxxxxf(3) 21 83 84 864-2 cumulative distribution function<<<=23,1231,211,2,)(FXxxxxxxx(1) (2)pdf (3)21XP(4) 21XP (5))25.1X5.(P<< (6))25.1X(P=(1) 121)(FXx21x)(Xxf12x121(2) <<=otherwise,...
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AB20040301 - 3-1 1234849496(1) 39(2) 2939(3) 2939(4)

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