Qualification > Math
CIE statistic2 doubts! Help please
Tohru Kyo Sohma:
--- Quote from: ~Alpha on July 30, 2011, 01:19:28 pm ---"...at a rate of 100 per hour"
60 mins => 100 cars
(a) Find the mean, we denote it by for a Poisson Distribution. [Equivalent of E(X)]
3 mins => 100/60*3 = 5 cars.
X is the random variable denoting the number of cars passing under the bridge during a 3 minutes interval.
Therefore, X ~ Po (5).
No cars -> X=0.
P (X=0) = e^(-5)*5^0/ 0!
= e^(-5)
Give your answer to 3 significant figures.
(b) Let the required time be n minutes.
Now, X is the random variable denoting the number of cars passing under the bridge during an n minutes interval.
= 100n/60 = 10n/6.
"...probability is atleast 0.25 that no car will pass under the bridge during that interval"
I will use 'G' to denote the greater or equal to sign: ,
and 'L' to denote the less or equal to sign: .
X ~ Po (10n/6).
P(x=0) G 0.25
e^(-10n/6) G 0.25
Take ln on both sides.
-10n/6 G ln 0.25
n L ln 0.25* (-6/10) [G changes to L because you are multiplying by a negative number]
n L 0.831
"At least", prob. should keep on increasing. Therefore, the value of e^(-10n/6) should be greater and greater, which will happen the smaller -10n/6 gets. e^(-no.)= 1/e^(no.)
Take the greatest value of n you can from the answer you obtained, i.e. n= 0.831.
Check by substituting n= 0.831 in e^(-10n/6). You will get a probability which is greater than 0.25, answer is correct.
It's advisable to check your answers for such types of questions in probability.
Question 8 is similar to question 7. Since you are self-studying, I would suggest you try question 8 by yourself by first understanding my procedures in question 7. Post your answer here so that I can check it for you. If you are still unable to do it, let me know, I'll do it then.
Hint for question 8: probability that 0 or 1 => Add P(x=0) and P(X=1).
I hope it's clear. If not, lemme know. :)
--- End quote ---
thanks alot alpha
the answer to a is correct
but the answer to b according to my textbook is 49.9s
i'll try out question 8 myself
how does the In button work?
again thanks alot
i'll +rep u soon...they're asking me to spread the love!
Alpha:
--- Quote from: Tohru Kyo Sohma on July 30, 2011, 05:45:13 pm ---thanks alot alpha
the answer to a is correct
but the answer to b according to my textbook is 49.9s
i'll try out question 8 myself
how does the In button work?
again thanks alot
i'll +rep u soon...they're asking me to spread the love!
--- End quote ---
X is the random variable denoting the number of cars passing under the bridge during an n minutes interval.
n= 0.831 mins
=0.831*60 s
= 49.86 s
= 49.9 s.
You're getting stressed, chill. ;)
You're welcome. :)
And it's okay. Don't worry about the +rep. Do quest.8 now. And show me what you did. :)
The only difficulty in S2 is that the chapters resemble each other. :D
Alpha:
And most important. :-[
Did you understand my explanation?
Tohru Kyo Sohma:
--- Quote from: ~Alpha on July 31, 2011, 11:43:20 am ---And most important. :-[
Did you understand my explanation?
--- End quote ---
i got most of it but the part about using In button.....i dunno how to use it!
Alpha:
--- Quote from: Tohru Kyo Sohma on July 31, 2011, 12:05:11 pm ---i got most of it but the part about using In button.....i dunno how to use it!
--- End quote ---
Oh yes, I forgot this part. ;D
It's ln, not In. Log e to the base of e. See on a scientific calculator. Chapter ref.: logarithms. :)
http://www.chem.tamu.edu/class/fyp/mathrev/mr-log.html
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