probability(4) 20點

2007-11-06 8:10 am

Suppose that two balanced dice are rolled.Let X be the sum of the two faces showing.
a)Obtain the PMF of the random variable X
b)Construct a probability histogram for X

In the game of craps, a first roll of a sum of 7 or 11 wins,whereas a first roll of a sum of 2,3,or12 loses.
To win with any other first sum , that sum must be repeated before a sum of 7 is rolled. Use part(b)and the FPF
to determine the probability of

c) a win on the first roll
d) a loss on the first roll

回答 (1)

魏王將張遼

2007-11-07 12:27 am

✔ 最佳答案

(a) The Probability Mass Function is:
P(X) = 1/36, if X = 2 or 12
P(X) = 2/36, if X = 3 or 11
P(X) = 3/36, if X = 4 or 10
P(X) = 4/36, if X = 5 or 9
P(X) = 5/36, if X = 6 or 8
P(X) = 6/36, if X = 7
P(X) = 0, otherwise.
(b) The histogram:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Nov07/Crazyprob1.jpg

(c) The win on the first roll, we have its probability equal to:
P(7) + P(11) since a total of 7 and 11 are mutually exclusive.
= 6/36 + 2/36
= 8/36
= 2/9
(d) The lose on the first roll, we have its probability equal to:
P(2) + P(3) + P(12) since a total of 2, 3 and 11 are mutually exclusive.
= 1/36 + 2/36 + 1/36
= 4/36
= 1/9

參考: My Maths knowledge

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