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## #1 2006-11-13 07:04:04

fangree01
Member
Registered: 2006-11-13
Posts: 11

### probabilty

Hi all,

This is my first time on here and post so hi and thanks in advance for your help!
I am in first year at uni doing probability and ststistics.
The question i am stuck on is:

What is the distribtion of the number of X of contaminated vials in the batch of size n if the overall contamination rate is p?

What is the expectaion of X?

The info i have is:
n=20
p=0.01

I think i am missing some info,  i have been told to do the binomial distribution, but i missed the lecture on that and i can't work it out!!

I would be greatful for any help and sorry if it makes no sense.

Thanks

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## #2 2006-11-13 09:12:44

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: probabilty

The expected value of a binomial distribution (n,p) is simply np.

So in your example, the expected number of contaminated vials is 20 * 0.01 = 0.2.

It's possible that your lecture might have had variance in it as well, so I'll throw in that the variance of a binomial distribution is np(1-p). If the lecture you missed didn't have that in it, then I bet one of your upcoming lectures will.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2006-11-14 04:16:21

fangree01
Member
Registered: 2006-11-13
Posts: 11

### Re: probabilty

Hi Mathsyperson,

Thanks for your help are you using p as θ is can they be the same thing?

Also can you help me with the first part:

What is the distribtion of the number of X of contaminated vials in the batch of size n if the overall contamination rate is p?

This was the part i never really got.  Thanks for the tip on variance.

Thanks

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## #4 2006-11-14 04:44:25

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: probabilty

Oops, I missed that first part.

For a random variable X, defined by the binomial distribution (n,p), the probability that x=X is given by nCx * p^x * (1-p)^(n-x).

As for using θ instead of p, I've never seen that before. But as long as we both mean the same thing then it doesn't matter. I'm using p as the probability of one specific vial being contaminated.

Why did the vector cross the road?
It wanted to be normal.

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