If X and Y are independent random variable...

• Dec 30th 2009, 12:29 AM
zorro
If X and Y are independent random variable...
Question : If X and Y are independent random variable with respective parameters $\lambda_1$ and $\lambda_2$
Calculate
i) P(X + Y = n)
ii) P(x=k|X+Y= n)
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I cant understand what to do .....
• Dec 30th 2009, 12:37 AM
mr fantastic
Quote:

Originally Posted by zorro
Question : If X and Y are independent random variable with respective parameters $\lambda_1$ and $\lambda_2$
Calculate
i) P(X + Y = n)
ii) P(x=k|X+Y= n)
----------------------------------------------------------------
I cant understand what to do .....

The first thing you need to do is tell us what the distributions of X and Y are (exponential, I suppose)

Nevertheless, no doubt somewhere in your notes there will be a theorem telling you what distribution X + Y follows when X and Y are independent.

Now use the distributions of X, Y and X + Y to do the necessary calculations.

Please show all your work if you're still stuck and need help.
• Dec 30th 2009, 09:28 PM
zorro
mR FANTASTIC
i dont know which one to use but doesnt $\lambda$ come in poisson

and if i am correct if X and Y are independent the
X+Y = Pr(X) + Pr(Y)

• Dec 30th 2009, 09:29 PM
matheagle
yea this is a poisson and I proved this 2 weeks ago.
Part b is a binomial that I proved here, twice.
It took one minute to find it...
http://www.mathhelpforum.com/math-he...tml#post420940
• Dec 31st 2009, 04:23 PM
zorro
I went thrgh the post but i wasnt able to understand ......please could u provide me with an alternate way or explain me what have u done??
• Dec 31st 2009, 07:33 PM
mr fantastic
Quote:

Originally Posted by zorro
I went thrgh the post but i wasnt able to understand ......please could u provide me with an alternate way or explain me what have u done??

It would have helped if you said in your original post that the distributions were Poisson.

The thread that has been quoted is detailed and complete. Unless there is something specific in it that you don't understand, you might have to accept that the question is beyond your current level of understanding.

There is a lot of background material that you need to understand in order to be able to make sense of everything in the thread. It has been suggested before and now I will suggest again that you are advised to review all the work you are assumed to have covered in the several years leading up to the level you are currently studying at.
• Dec 31st 2009, 08:35 PM
matheagle
I guessed Poisson by the lambda, but it couldn't have been exponential or any continuous distribution because of P(X=k|anything)=0.

AND Zorro, you need to state the complete questions.
You asked a hypothesis question today and no one can make a decision without alpha.
We can obtain the p-value, but we can't decide on which hypothesis without the prob of making a type one error.
• Jan 1st 2010, 01:28 AM
zorro
sorry and will keep in mind
• Jan 1st 2010, 04:14 AM
zorro
in the link provided how did he conclude that Pr(U|U+V=n) in my problem i have to prove that part ......i guess