Probability and Statistics #1

a)X min. = 1 + 1 + 1 = 3X max. = 1+1+2+2+3+3+4+4+5+5+6+6+6 = 48
b)P(Y=3)
= P(1,1,1) + P(2,2,2) + P(3,3,3) + P(4,4,4) + P(5,5,5) + P(6,6,6)
= 6 (1/6)³
= 1/36
c)P(Y=4)= Σ P(A,A,A,B)= (4C3)(1/6)^4 * 6P2= 5/54
d)P(x ≤ 5)= P(1 , 1 , 1) + P(2 , 1 , 1 , 1) = (1/6)³ + (4C3)(1/6)^4= 5/648
e)P(X=8)= P(5 , 1 , 1 , 1) + P(2 , 3 , 1 , 1 , 1) + P(1 , 1 , 2 , 2 , 2)= (4C3) (1/6)^4 + (5!/3!) (1/6)^5 + (5C3) (1/6)^5= 1/144


2011-03-09 20:14:57 補充：
c) to e) have some mistake.....

2011-03-09 20:32:36 補充：
唔知點解補充不到,打在意見 :

Corrections :

c)

P(Y=4)
= Σ P(A,A,B)A ........... since the last one must be A
= (3C2)(1/6)^4 * 6P2
= 5/72

2011-03-09 20:32:59 補充：
d)

P(x ≤ 5)
= P(1 , 1 , 1) + P(2 , 1 , 1) 1 ........... since the last one must be 1
= (1/6)³ + (3C2)(1/6)^4
= 1/144

2011-03-09 20:33:20 補充：
e)

P(X=8)
= P(5 , 1 , 1) 1 + P(2 , 3 , 1 , 1) 1 + P(1 , 1 , 2 , 2 ) 2
= (3C2) (1/6)^4 + (4!/2!) (1/6)^5 + (4C2) (1/6)^5
= 1/216

What's the mistakes ar?