[問題] 走棋盤的問題(joint pmf)
大家好，小弟初學統計，最近碰到這題Hogg書上的練習題一點頭緒都沒有，想請問
版大們這題應該往哪邊去想或怎麼做比較好@@"
Q: 一個粒子從(0,0)開始往東或西或南或北移動，每一次移動都是獨立的事件，往每
一個方向移動的機率均為1/4，總共移動3次。 令S等於東西向位置、T為南北向位置。
(a) 定義S和T在n=3時的joint p.m.f，以及joint p.m.f.和marginal p.m.f下的機率。
(b) 令X=S+3, Y=T+3，X和Y是如何分配的。
因為n只有3所以勉強可以用圖想，甚至把每個機率弄出來
ex. -> -> -> or -> <- -> 之類的
^
o |
o o o |
o o o o o |
o o o x o o o |
o o o o o |
o o o |
o |
S -------------> T
但如果數字很大好像就沒辦法算了..麻煩大家了!
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附上原文:
A particle starts at (0,0) and moves in one-unit independent steps with
equal probabilities of 1/4 in each of the four directions: north, south,
east, and west. Let S equal the east-west position and T the north-south
position after n steps.
(a) Define the joint p.m.f. of S and T with n = 3. And give the probabilities
of the joint p.m.f. and the marginal p.m.f.'s.
(b) Let X=S+3 and let Y=T+3. How are X and Y distributed?
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