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Hello, if I had 100 different sequences of sets of numbers sequence one- 246412431................................bimodal - 236511213sequence two - 331564115.......................would this be bimodal or multimodal distribution?
Quote from: Thebox on 13/04/2015 19:44:02Hello, if I had 100 different sequences of sets of numbers sequence one- 246412431................................bimodal - 236511213sequence two - 331564115.......................would this be bimodal or multimodal distribution?So, 100=3 different sequences?sequence one- 246412431=9So do the others, so they are all the same, yes.Good, thought I'd got it==========Seriously, are you looking for a genuine answer? I haven't even bothered to look at this one due to a suspicion that any answer will be met with a rebuttal (binomial is book learning and complacent thinking) followed by an invented theory of probability.
2 dice would have a 6^2 chance of rolling the same number
Quote from: Thebox on 13/04/2015 19:44:022 dice would have a 6^2 chance of rolling the same numberNo. If A rolls any number, B has a 1/6 probability of rolling the same number. So "any double" is 1/6 but a specific double is indeed 1/36.And "binomial" is not the same as "bimodal".
Sorry binomial was a typo in the title I did not know how to correct.
Just to back up what Alan is saying:Let's take a simple example which is similar to your dice rolling. You have 2 coins which you toss one after the other. Clearly the chance of 2 heads is 1/4. But if you toss the 1st coin and get a head, what is the probability of getting 2 heads? Many people will say 1/4, but as you know the probability that the 2nd coin will fall heads is 50%, 1/2. So it depends when you make your decision or bet. In the case of the rolling dice, once the first 1 has appeared the probability of the second is as Alan says 1/6, but that is the same for both players. Unless you are saying the 2nd player is only allowed to bet on the total outcome before any dice is rolled, whereas the 1st player has a bet after the first roll. In this case yes, the probabilities are different for each player.Quote from: Thebox on 21/04/2015 18:09:32Sorry binomial was a typo in the title I did not know how to correct.It's a pity your spelling mistake wasn't the other way round!The rolling of 2 dice can create a binomial distribution, with a mode of 7, if you add the face values of the 2 dice. The individual dice have an equal chance for each face, so this is a random distribution and has no mode. While I have your attention I will make a small point. Although we might discuss dice or coins, one of the strengths of maths and science is that we can take something specific and then remove the numbers describing the outcomes and develop a theory which is independent of specific objects, just using numbers and symbols on their own. So what is true for dice can be applied to children in a school, queues in a bank, or traffic approaching an intersection. But while considering the theorems, we do not need to specify particular objects. Just a small point 
just to confirm1/221 is not the same as 4524/1,000,000?
Quote from: Thebox on 21/04/2015 20:19:16just to confirm1/221 is not the same as 4524/1,000,000?To use a technical term "it is near as dammit"It all depends what you are doing.If parking a car this difference is unlikely to trouble you, but if you are manoeuvring a sample under an electron microscope, different story.
I will redefine for yourandom x has 52 variants and the probabilities of receiving (a) from x is 1/221random x + random x =2/442
Flirts of all congratulations in spotting the f.point's new maths is in fact a reinvention of std vector maths (albeit in 1 dimension).I've left a couple of questions there for you. One is easy, the other less so, have a think.Quote from: Thebox on 22/04/2015 12:13:12 I will redefine for yourandom x has 52 variants and the probabilities of receiving (a) from x is 1/221random x + random x =2/442In probability, definitions are vital, so good start. Some questions:Are you saying that the set of items called x contains 52 items all different? Or are you saying x contains 221 items but only 52 different types of item?I assume (a) is any single item selected from x.
I am referring to texas holdem poker, and x contains 52 different variants, (a deck of cards).(a) being pocket pair aces for example purposes.
Quote from: Thebox on 22/04/2015 16:40:31I am referring to texas holdem poker, and x contains 52 different variants, (a deck of cards).(a) being pocket pair aces for example purposes. Thanks for the clarification.Not sure what a pocket pair ace is, but as I'm unlikely to play it tells me this isn't info I need to know.Sounds as though you should be an expert on probability!Enjoy your games
pocket pair aces is 2 aces as your starting hand you are dealt , so you know.