Monday, March 14, 2005
ERBA= Exams Really Bite Ass
Just got out of the ERBA exam. BLECH. It was comprised of three questions, decreasing in difficulty/impossibility from 1 - 3. After doing the post-exam, confidence-shattering exchange of answers, I realized that most everybody had difficulty with the exam. Of course, I was seated next to Yoav, who, upon reading the first question said, "Yeah!" under his breath. (Yoav, if you're reading, know that I am scratching my nose with a specific finger right now.)
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4 comments:
Mmm, beer. ;)
You want the probability of getting more than 6mg/10^3L or more than 0.006mg/L. That's 1 - probability of getting less than 0.006mg/L.
The probability of getting less than 0.006mg/L is directly from the cumulative density function, which is 1-e^(-lambda*x) for the exponential distribution. Let x = 0.006, lambda = 1 / mean = 1/0.002 = 500, calculate 1-e^(-500*0.006) = 1-e^(-3) = 0.95. That's the probability of getting less than 0.006, so you want 1-0.95 = 0.05, so 5% or so was my answer to 1a.
1b follows pretty easily from 1a. I use Poisson but I guess binomial can be used as well. Let N=3, find the proability for k=0 and for k=1, and their sum is the probability of at most once during three days. It ends up being virtually 1.
1c was easy and doesn't depend on 1a or 1b. The mean is given (0.002), and for exponential standard deviation = mean = 0.002. Then Z = (0.006-0.002)/0.002 = 2, and it's a straight lookup in the normal distribution table from there, giving 0.0228 or 2.28% result, significantly smaller than 1a.
Do I get to pick a type of beer even if I'm wrong? ;)
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