離散-著色多項式&機率

用聯集的方法 ,算出來為λ*(λ-1)*((λ-2)^3)

但覺得怪怪的

想請問著色多項式是唯一嗎?

因為自己對圖上λ

先對右上角上λ

最上面λ-1

左下角λ-1

其他兩點λ-2 , λ-2

結果為λ*((λ-1)^2)*((λ-2)^2)

是我哪邊搞錯了嗎

6. (10%) A pair of fair dice is continuously rolled until either a 1 or a G

appears at which point the experiment stops. What is the probability

that the experiment was stopped not because of 1's appearance?

結束的情形可能為 (1,x), (x,1),(6,x) (x,6) 其中x=1,2,3,4,5,6 總共有20種可能

其中去掉包含1的可能 (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) (2.1) (3.1) (4.1) (5.1) (6.1)等11種

所以1不出現的情況下結束的機率為 9/20

7. (10%) Suppose P balls are distributed at uniformly random into N

boxes. Let Xi be a random variable defined by Xi = 1 if box i is

einpty and Xi = 0 otherwise. Compute E(Xi), the mean of Xi. What

is expectation of the number of einpty boxes after these P balls were

distributed.

請這題的機率要怎麼設呢?

請各位高手 與助教指點迷津