Probability

1 Let X be the no. of days that John goes to Circle-K before he goes to 7-11 Then X follows gometric distribution with p=0.4. E(X)=q/p=0.6/0.4=3/2.

(b) The probability is just equal to 1-p(0)-p(1)-p(2)=1-0.4-(0.4)(0.6)-(0.4)(0.6)^2=0.2736

2010-12-11 18:25:57 補充：
1(a) should be X follows gometric distribution with p=0.6. E(X)=q/p=0.4/0.6=2/3.

2010-12-11 21:29:57 補充：
geometric dist. has two different forms. One for x=0,1,2,... and one for x=1,2....

(a)
不指明考慮的連續天數是不能計算的，因為隨著考慮的連續天數趨近於無限，其結果也會趨近於無限。

(b)
Σ(n = 3 to ∞)0.6ⁿ0.4

(2) The formula is correct, just the calculation is wrong
1 - 0.4 - 0.24 - 0.144 = 0.216