16/11更新Stat QuestionsX1[趕急] [復制鏈接]

Let the probability density function of Y be

            cy exp(-2y),     0<=y<無限;
f(y)=
            0,                     elsewhere.

where c is a constant.

(a) Find the value of c that makes f(y) a density function. (not yet confirmed ANS:2)
(b) State the distribution of Y, and give the mean and varience for Y.
(c) Write down the moment generating function for Y.

1. (5C2)/(9C6)=10/84=0.1190
2.[(n-r-1)! *r!]/ n!

唔係好記得點systematic地solve lu,但係應該無錯

引用第1樓hohoho2於2011-09-23 14:38發表的“”:
1. (5C2)/(9C6)=10/84=0.1190
2.[(n-r-1)! *r!]/ n!
唔係好記得點systematic地solve lu,但係應該無錯

可不可以簡單講下第一條個答案點黎

probability = no of favourable outcome/total outcome
講左點計total outcome先
呢隻係combination with replacement
有個例子係當你有 3 個波要放落 3 個格,每個格可以放多過一個波 ,問有幾多種排法
呢個時候你可以當係有3個波同3-1 = 2條分隔線排次序
OOO||
OO|O|
OO||O
O|OO|
O|O|O
O||OO
|OOO|
|OO|O
|O|OO
||OOO

10種排法

其實如果全部都理order o既話本身有5!=120咁多種排法,但係你會發現到本身5種排法入面果3粒波之間o既order係無用的,呢到每個排法整多左3!個combination出黎,另外果兩條分隔線個order都係唔使理,呢到每個排法又多左2!個combination
所以total outcome=5!/(2!x3!)=10,即係5C3
或者3(個波)+(3-1)(條分隔線) C 3(波既數量)
當波數係k,格數係n
total outcome就係(n+k-1)Cn <----formula

你呢到有6個波同4個格,即係有9C6個outcome=84

然後計favourable outcome
有邊個係favourable outcome?
每個格最少有1個波,所以有4個波o既位置係fix左,然後剩番兩個亂排出黎果o的結果就係favourable outcome
呢個時候你可以當係2個波4個格咁睇,(2+4-1)C2=5C2=10

大約係咁la

BTW今日有同學拎住份assignment問我同樣呢兩條問題

引用第4樓hohoho2於2011-09-25 01:00發表的“”:
BTW今日有同學拎住份assignment問我同樣呢兩條問題 [表情] [表情] [表情] [表情] [表情] [表情] [表情]

咩同學= =

引用第5樓vincent於2011-09-25 01:27發表的“”:
咩同學= =

大學同學lor

引用第0樓vincent於2011-09-22 22:49發表的“Statistics Questions (each 250好友元)”:
1)
Assume that every time you buy an item of the HK Disney series, you receive one of the four types of cards, each with a cartoon character Mickey, Minnie, Donald and Daisy with an equal probability. Over a period of time, you buy 6 items of the series. What is the probability that you will get all four cards?
2)
If n persons, including A and B, are randomly arranged in a straight line, what is the probability that there are exactly r persons in the line between A and B?

我既答案:

1.) (4P4 x 6P2) / (4C1)^6 = 0.176

2.) 同hohoho一樣

引用第7樓happykinghk於2011-09-25 15:04發表的“”:
我既答案:
1.) (4P4 x 6P2) / (4C1)^6 = 0.176
.......

咁應該你o岩了,我好似貪快照sub formula無理到o的outcome係with unequal probability

引用第8樓hohoho2於2011-09-25 17:09發表的“”:
咁應該你o岩了,我好似貪快照sub formula無理到o的outcome係with unequal probability [表情]

做咩咁客氣
其實我都唔肯定，諗住一齊研究下咁解

呢兩條係elementary 既 prob題目黎

引用第10樓fatman於2011-09-25 18:05發表的“”:
呢兩條係elementary 既 prob題目黎 [表情]

嗯

happykinghk
hohoho2

謝謝

題目更新了
希望大家幫幫手
好急但唔識做

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