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Old 2011-07-14, 10:37   #1
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Default Help with probability distribution.

Hi. I have a math problem and in desperate need for help.

Imagine that you roll a dice 9 times. Let X stand for the number of sixes you get on those rolls.

What is the probability distribution of X?
What is the probability of you getting maximum 1 six?
What is the probability of you getting at least 3 sixes?


I'm thankful for all help :)
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Old 2011-07-14, 11:56   #2
R.D. Silverman
 
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Quote:
Originally Posted by Unregistered View Post
Hi. I have a math problem and in desperate need for help.

Imagine that you roll a dice (sic) 9 times. Let X stand for the number of sixes you get on those rolls.


What is the probability distribution of X?
I suggest that you read a basic book on probability and statistics.
We can recommend some, if you like.

The term "probability distribution" is nonsense at worst and poorly
defined at best. Do you mean density function (pdf), or do you mean
cumulative distribution function (cdf)?

In either event, the answer to your question will be found in
any book on probability. Also, repeat after me: Google is my friend.

Quote:


What is the probability of you getting maximum 1 six?
What is the probability of you getting at least 3 sixes?
Finding the answer to these is easy once you have done some basic
reading. Noone is going to do your homework for you.


I recommend Hogg & Craig as a good book.
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Old 2011-07-14, 12:38   #3
wblipp
 
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Quote:
Originally Posted by Unregistered View Post
Hi. I have a math problem and in desperate need for help.

Imagine that you roll a dice 9 times. Let X stand for the number of sixes you get on those rolls.

What is the probability distribution of X?
What is the probability of you getting maximum 1 six?
What is the probability of you getting at least 3 sixes?


I'm thankful for all help :)
It goes by the name Binomial distribution. From that you should be able to find the formula for exactly X sixes. The other two answers come from adding up some of these values.
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Old 2011-07-14, 14:22   #4
R.D. Silverman
 
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Quote:
Originally Posted by wblipp View Post
It goes by the name Binomial distribution. From that you should be able to find the formula for exactly X sixes. The other two answers come from adding up some of these values.
Give someone a fish and they eat for a day.
Teach someone to fish and they eat for a lifetime....

It is better to teach someone how/where to find answers for
themselves rather than just handing them the answer.
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Old 2011-07-14, 15:12   #5
wblipp
 
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Quote:
Originally Posted by R.D. Silverman View Post
Give someone a fish and they eat for a day.
Teach someone to fish and they eat for a lifetime....

It is better to teach someone how/where to find answers for
themselves rather than just handing them the answer.
You told him "go fish." I showed him how to use a fishing pole. Neither of us gave him a fish.

We have very different opinions about what constitutes "handing him the answers." He asked a trivial question and you told him to go read a whole book. I told him what to look up in the index - he still has to read and understand the information. You told him to google, I told him what to google. He still has to find it and understand it.
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Old 2011-07-14, 15:27   #6
davieddy
 
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Quote:
Originally Posted by R.D. Silverman View Post
Give someone a fish and they eat for a day.
Teach someone to fish and they ....
...die of hunger, boredom or fright.

Probabilty of the first 3 throws being a six and the remaining
6 throws not being a six is (1/6)3 *(5/6)6

There are 9!/(6!3!) ways of placing the 3 sixes (hence "Binomial" distribution).

Last fiddled with by davieddy on 2011-07-14 at 15:28
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Old 2011-07-14, 15:31   #7
science_man_88
 
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Quote:
Originally Posted by wblipp View Post
You told him "go fish." I showed him how to use a fishing pole. Neither of us gave him a fish.

We have very different opinions about what constitutes "handing him the answers." He asked a trivial question and you told him to go read a whole book. I told him what to look up in the index - he still has to read and understand the information. You told him to google, I told him what to google. He still has to find it and understand it.
plus you gave them a term they hadn't heard of it appears so if that's the case they will still have to look it up to solve it unless davieddy continues to give more hints.
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Old 2011-07-14, 16:05   #8
davieddy
 
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plus you gave them a term they hadn't heard of it appears so if that's the case they will still have to look it up to solve it unless davieddy continues to give more hints.
Prove you can get the answer without any more hints.
I suspect the excercise comes from a chapter entitled
"Binomial Distribution".

BTW I was being intentionally helpful, in support of WBLipp.

This isn't the homework forum, and the poster sounds as if
(s)he is beyond "help" anyway.

David
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Old 2011-07-15, 00:35   #9
Christenson
 
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This problem can also be solved with combinatorics....keeping the die rolls in order, there are 6^9 possible sequences of 9 rolls of six sided die...if you count the number of them with one six, you have the odds of a single six....

That is, suppose the six is in the first position...there are then 8^5 ways for the remaining 8 rolls to fall and leave you with exactly one six....

This should give an idea of what to do....

And RDS: Your effort is appreciated. Thank you.
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Old 2011-07-15, 06:43   #10
lavalamp
 
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Quote:
Originally Posted by R.D. Silverman View Post
Do you mean density function (pdf)
Actually, since in this case X is a discrete random variable, it has a probability mass function (PMF).
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Old 2011-07-15, 07:23   #11
xilman
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Quote:
Originally Posted by R.D. Silverman View Post
Give someone a fish and they eat for a day.
Teach someone to fish and they eat for a lifetime....
Light someone a fire and they are warmed for a day. Set someone on fire and they are warmed for the rest of their life.
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