Are It True?
Thread Starter
Registered User
Joined: Jul 2001
Posts: 6,592
Likes: 0
From: Yorba Linda, CA
When you are computing an expected value, it is the expected value of the pair of envelopes in the game. You're absolutely correct that the calculation is valid whether he holds the more-valuable or the less-valuable envelope; it is also irrelevant to the player in either case. When I'm computing an expected value, it is not the expected value of the pair of envelopes in the game, it is the expected value of the remaining envelope in the game: the envelope that is not in the player's possession. That's where your analysis and mine differ.
And that's where your analysis falls short. The player in the game has to determine whether the other envelope is more or less valuable than his, and by what amount it is more or less valuable. Therefore, he computes the expected value of that single envelope. This calculation results in the 5X/4 figure.
In no way is this "bunk", as you call it. When you buy a lottery ticket, for example, you may compute the expected value of the ticket (probability of winning times value of winning) and compare that expected value to the cost of the ticket: if E(winning) > cost, you buy the ticket; if E(winning) < cost, you don't.
Earlier you stated that I did not model a situation accurately, when I was trying to simplify the expected value idea by adding up 100 results. I did, actually, in a manner that simplifies the computations for the mathematically challenged, much as one would use a simple d = 1/2 at^2 model--neglecting air resistance--when teaching beginning physics or calculus students. Suppose you set up an experiment as follows:
You have 10,000 pairs of envelopes: 5,000 sets of $5/$10 pairs and 5,000 sets of $10/$20 pairs. These pairs are randomly shuffled. The first of the 100 players selects a pair of envelopes, and then selects one of the pair. A disinterested, poker-faced moderator opens the selected envelope. If it contains $10, he gives it to the player and moves on to the next player. If not, he discards the pair and the player selects another pair. This continues till all 100 players have selected a pair of envelopes, each having an envelope worth $10.
We now have a situation exactly as I presented, where each of 100 players has an envelope worth $10, and there is a 50-50 chance that the $10 is the higher value or the lower value. Nothing is improbable, and in every case there are exactly two envelopes involved.
I grant you that it takes a convoluted approach like this one to achieve the end, but the manner in which you get there is completely beside the point. The situation was given to simplify the discussion about expected value and for no other purpose. Whether it takes a tremendous amount of machinery to create a simple situation is irrelevant.
And that's where your analysis falls short. The player in the game has to determine whether the other envelope is more or less valuable than his, and by what amount it is more or less valuable. Therefore, he computes the expected value of that single envelope. This calculation results in the 5X/4 figure.
In no way is this "bunk", as you call it. When you buy a lottery ticket, for example, you may compute the expected value of the ticket (probability of winning times value of winning) and compare that expected value to the cost of the ticket: if E(winning) > cost, you buy the ticket; if E(winning) < cost, you don't.
Earlier you stated that I did not model a situation accurately, when I was trying to simplify the expected value idea by adding up 100 results. I did, actually, in a manner that simplifies the computations for the mathematically challenged, much as one would use a simple d = 1/2 at^2 model--neglecting air resistance--when teaching beginning physics or calculus students. Suppose you set up an experiment as follows:
You have 10,000 pairs of envelopes: 5,000 sets of $5/$10 pairs and 5,000 sets of $10/$20 pairs. These pairs are randomly shuffled. The first of the 100 players selects a pair of envelopes, and then selects one of the pair. A disinterested, poker-faced moderator opens the selected envelope. If it contains $10, he gives it to the player and moves on to the next player. If not, he discards the pair and the player selects another pair. This continues till all 100 players have selected a pair of envelopes, each having an envelope worth $10.
We now have a situation exactly as I presented, where each of 100 players has an envelope worth $10, and there is a 50-50 chance that the $10 is the higher value or the lower value. Nothing is improbable, and in every case there are exactly two envelopes involved.
I grant you that it takes a convoluted approach like this one to achieve the end, but the manner in which you get there is completely beside the point. The situation was given to simplify the discussion about expected value and for no other purpose. Whether it takes a tremendous amount of machinery to create a simple situation is irrelevant.
Thread Starter
Registered User
Joined: Jul 2001
Posts: 6,592
Likes: 0
From: Yorba Linda, CA
[QUOTE]Originally posted by tokyo_james
Sorry to drag this back from the dead .... I just found it again ......
Do you need to write is as "Identification of risk and mitigation of risk" ??
Sorry to drag this back from the dead .... I just found it again ......
Do you need to write is as "Identification of risk and mitigation of risk" ??
Thread Starter
Registered User
Joined: Jul 2001
Posts: 6,592
Likes: 0
From: Yorba Linda, CA
("games plans"? A typo, I hope.)
Your example is more complicated because you are using the verb "to be" in a different sense: your predicate is a noun, not an adjective. You are using the verb to mean "constitute" or "form"; I'm using the verb to mean "possess the quality of being". (Note that you felt it necessary to change from "game plan" to "games [sic] plans" when you used the plural verb.)
Would you write "Defence and counter-attack constitutes the game plan."? I think not; no more than you would write "The first baseman, the second baseman, the shortstop and the third baseman is the infield."?
When the subject is a collective noun, Americans and Englishmen tend to disagree on which form of the verb to use: an American would likely say "The band is on stage." whereas an Englishman would likely say "The band are on stage." This is a different issue than the one we're discussing, but it's related.
Your example is more complicated because you are using the verb "to be" in a different sense: your predicate is a noun, not an adjective. You are using the verb to mean "constitute" or "form"; I'm using the verb to mean "possess the quality of being". (Note that you felt it necessary to change from "game plan" to "games [sic] plans" when you used the plural verb.)
Would you write "Defence and counter-attack constitutes the game plan."? I think not; no more than you would write "The first baseman, the second baseman, the shortstop and the third baseman is the infield."?
When the subject is a collective noun, Americans and Englishmen tend to disagree on which form of the verb to use: an American would likely say "The band is on stage." whereas an Englishman would likely say "The band are on stage." This is a different issue than the one we're discussing, but it's related.
Banned
Joined: Jul 2003
Posts: 425
Likes: 0
From: Heaven,
Originally posted by S2020
I is smart but I is not understand..
I is smart but I is not understand..
I is sorta understand the post. 
Magician are must is a new-coming immigrant.
I take it back. His other posts seem to be of proper grammar. 
Thread
Thread Starter
Forum
Replies
Last Post