Portfolio Type II -- Modelling Probabilities in Games of Tennis

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When Adam and Ben play against each other in tournaments outside the club, their point-winning probabilities remain the same (2/3 and 1/3 respectively), but the rules now require that players win by 2 points and therefore, that games may in theory be infinitely long

Show that although Adam's point odds agains Ben are 2:1, his game odds are almost 6:1. Be sure to consider separately the cases of non-deuce and deuce games

This question is a toughie anyone out there willing to contribute some of their imput on this question

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Hi can anyone who is familiar with this portfolio explain what is the random variable being asked for, if it is not Y...and is the probability model being asked some sort of function or do we just graph the distribution? The question is a bit vague:

2. When Adam and Ben play against each other in club events, their probabilities of winning points are approximately the same as above. In club play, the tennis rules are generally followed (win with at least four points and by at least two points in each game), but to save court time, no game is allowed to go beyond 7 points. This means that if deuce is called (each player has 3 points), the next point determines the winner. Show that there are 70 possible ways that such a game might be played. To assist with this let Y be the number of points played. What values can Y take? For each possible value of Y find the number of possible ways that such a game could be played, and show the probability model for such a game. Be sure to define a random variable for the distribution.

Thanks

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Yeah I'd like to know the answer to this question as well. What "model" are they looking for?

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Well, for a game to end, there must be 4, 5, 6 or 7 points scored. For each of these numbers, I'm assuming you need to show a probability model for the different outcomes. Ie, for a 4 point game, you know that there are only two ways for it to happen.

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Hi can anyone who is familiar with this portfolio explain what is the random variable being asked for, if it is not Y...and is the probability model being asked some sort of function or do we just graph the distribution? The question is a bit vague:

2. When Adam and Ben play against each other in club events, their probabilities of winning points are approximately the same as above. In club play, the tennis rules are generally followed (win with at least four points and by at least two points in each game), but to save court time, no game is allowed to go beyond 7 points. This means that if deuce is called (each player has 3 points), the next point determines the winner. Show that there are 70 possible ways that such a game might be played. To assist with this let Y be the number of points played. What values can Y take? For each possible value of Y find the number of possible ways that such a game could be played, and show the probability model for such a game. Be sure to define a random variable for the distribution.

Thanks

Do you mind providing the first question? It's kind of hard to do it without the firsto ne...

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well i'm working on this specific IA as well.

as far as i've progressed we need to have a binomial distribution here.

as smo mentioned above, you've got 4 types of games ending with 4,5,6,7 scores each.

In each case you should have a binomial distribution for the scores before the final score.

For example, with the game ending with 6 scores. We know that once the final score is scored the game ended, so the winner cannot score 4 before 6 scores has been scored. In other word, we leave the final score until the last minute.

so, not counting the 6th scores we have 5 balls scored. 3 would be for the winner and 2 for the loser.

the binomial distribution will be binompdf(5,2/3,3)

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I just finished this at 3:00 a.m. Eastern US time. Very straightforward, and I thought rather easy for a Type II. Make sure to get the formula for deuce correct in the final stages, as that is where many of my friends messed up. I think it looks a lot better to the scorer when you put your n C r in terms of Y, instead of listing the exact numbers everytime or just putting n or r. Also, realize that to win a game, the person !must! win the last point, so you do not need to factor that into your calculations.

Edited by DawgSideoftheMoon

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I just finished this at 3:00 a.m. Eastern US time. Very straightforward, and I thought rather easy for a Type II. Make sure to get the formula for deuce correct in the final stages, as that is where many of my friends messed up. I think it looks a lot better to the scorer when you put your n C r in terms of Y, instead of listing the exact numbers everytime or just putting n or r. Also, realize that to win a game, the person !must! win the last point, so you do not need to factor that into your calculations.

It was very straightforward. Unfortunately, for my class, we finished learning binomial distributions about 3-4 days after we had received the portfolio, so in this aspect, it was more difficult than it should have been.

When you're working on Q5, look to Q6. It provides some rather large hints.

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i just got assigned this portfolio. and i'm really stuck on #2

We never learned stats properly, so i'm kinda lost. Does anyone know how to figure out the 70 possible ways.??

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You could list them for starters... only 35 ways when you really get down to it.

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It was very straightforward. Unfortunately, for my class, we finished learning binomial distributions about 3-4 days after we had received the portfolio, so in this aspect, it was more difficult than it should have been.

When you're working on Q5, look to Q6. It provides some rather large hints.

i realize that we have to use the sum of an infinite geometric series...and something along the lines of stochastic processes..but after that i'm stuck. T_T;; any hints? thanks =]

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i realize that we have to use the sum of an infinite geometric series...and something along the lines of stochastic processes..but after that i'm stuck. T_T;; any hints? thanks =]

Say what? Look at Q6 and split up the probabilities into 3 parts: prob of winning if non-deuce, prob of deuce, and prob of winning if deuce (basically what Q6 says).

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can we start at the beginning of this IA... im just a bit confused to start

lol i just finished this last wednesday...good luck with it. I admit it's confusing at first, but if you review your probability you'll be fine later on. Don't think too complex, i realized that the solution was often easier than I perceived it to be...lol (wasted alot of brain cells for nothing T_T)

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so how do you find the probability of winning once deuce is called, since there are infinite possibilities/combinations?

parts one and two were quite simple, but then part three is confusing. I don't know where to start...

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I'm trying to get this done, but I've been running into some silly problems early on (in part one) .

Can someone confirm whether my thought process is correct for number one.

I used binomial distribution and I found the probability distribution for each player winning x number of games.

Then, I used the expected value formula np, and I got the success chance.

Then, using the expected value as the mean, and n as delta f, I found the standard deviation.

Sorry, my probability is kinda rusty. A confirmation would be great.

Edited by LinuxBeta

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^^^ Yes, your values are correct.

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Thanks for the confirmation, Irene. Big confidence boost right there.

I just finished number 5, and I have another question. Is it normal for my probabilities not to add up to 1? Did I make a mistake somewhere?

I'm something like 12/729 off...which is negligible...I suppose, as long as the examiner does not notice.

Edited by LinuxBeta

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If it doesn't add up to 1.00, you've made a mistake. I think I made the same mistake... took me a whole day to figure it out!

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Yay, I found it. It really was a stupid mistake...forgot to multiply by 2...which led to my probability of Adam winning to be intact, but for the one of him losing to be too small. The irony is that I was just about to type another message, saying that I couldn't find the error...and I started to explain my thought process...and then I realized my fatal flaw.

Also, I am now finished with this portfolio. It really wasn't that difficult...and it wasn't as long as some of my previous ones. However, there really are a lot of places you can mess up, which will kill your calculations later on. Always make sure your probabilities add up to 1. =P

Edited by LinuxBeta

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It is amazing how simple this seems in retrospect, after you figure out the "trick".

thank you all for insisting on the idea of infinite geometric series .

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