Question 1127739: Dunwich Hamlet A young and purely fictitious football team Dunwich Hamlet 1 has two types of fans. One type is a hardcore football aficionado, who buys season tickets and rarely misses games. The other type is a typical resident of Dunwich village, who supports his local team but does not go to the games very often himself. Dunwich is a family-friendly club and each ticket holder is allowed to bring a family member for free. Now the first season comes to an end and the club chairman would like to thank season ticket holders and invite them to a party. But alas the club accounting is not very mature: the database on season ticket sales was lost in an unfortunate accident2 and no one has ever counted tickets sold on the day
. 1Not to be confused with Dulwich Hamlet or Dunwich Dynamo.
2Dog ate chairman’s notebook
However, the chairman holds every copy of Non League Paper which covers Dunwich games and the paper accurately reports the number of spectators for each game. Can he get a good estimate of how many season ticket holders there are from these data? The model and questions. There are a season ticket holders and b “normal” fans. For each game each fan independently decides whether to go to this game or not. The probability for the season ticket holder to attend the game is pa and for the “normal” fan it is pb. The prior distributions on a and b are uniform distributions on [amin, amax] and [bmin, bmax] respectively. Let cn be the total number of ticket holders for the n-th game.
(a) Describe the distribution of the number of ticket holders attending the n-th game p(cn|a, b). What are its mean and variance?
(b) Each ticket holder (independently) with probability pd brings a family member. Let dn be the total number of fans at n-th game (this is the number reported in the paper). What is the mean of the distribution p(dn|cn)?
(c) Draw the graphical model corresponding to this setup (the variables are a, b, c1, c2, . . . , cN , d1, d2, . . . , dN ).
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
I waited very patiently, while this post vent "out of scope".
Now, when it finally did, let me express my thoughts regarding this post.
In my life I saw tens of thousands of Math problems, and solved thousands of them.
But I never saw a truly Math problem longer than 5 lines of standard text.
I think that such creations as in this post are not Math problems at all.
They relate to some other areas of human activity - to writing novels, probably.
Why did I write my response ? - With the only one goal to explain you THIS:
Do not spend your time for nothing, posting so long printing to this forum.
In any case, nobody will even read it.
What is even worst, I can not imagine the person/(the tutor) with his (or her) mind tuned on Math, who will read
one single full line of this text - so boring and nonsensical it is.
Why do I write it ?
- Because so long posts still continue to be posted to the forum.
There is one simple truth: no one person will read the text longer than 5 lines, if it is not EXCEPTIONALLY interesting.
"S'est la vie", or, speaking in other words, the life is established in this way.
This post is DEFINITELY not so interesting to spend the time reading it.
Now that's all.
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