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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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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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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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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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