Recent content by exk

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    Stats: finding probability in normal distribution

    Z is not the mean, it is the standard normal random variable. You want to find P(Z > z0). So you want to find P(Z<z0) such that it equals to 1-P(Z>z0). 1-0.1234=0.8766, which corresponds to about z0=1.155 from the table David posted
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    Probability of At Least One Non-Defective Bulb Selected from Company's Stock

    Actually there are specifically 2 bulbs that you are dealing with so when calculating the probabilities you have C(2,0) and C(2,1) which I didn't put explicitly, but are in the calculations I mentioned.
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    I think of it as hard proof by induction

    As Dick mentioned induction may be the way to go: a_2=2^{\lambda} Take your expression now and show that the statement is true for n=2 (I guess this is also your inductive hypothesis): \frac{(a_n^2+1)^{\lambda}}{a_n^{\lambda}}-2^{g(n)} \geq 0 --> \frac{(a_n^2+1)}{a_n} \geq...
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    Probability of At Least One Non-Defective Bulb Selected from Company's Stock

    Your problem doesn't state how many bulbs were manufactured total so you can't assume it's 100, hence your solution is wrong. I think the following might work better for you: Let X= # of defective bulbs. Then you want to find P(X=<1)=P(X=0)+P(X=1) P(X=0)=.96^2 P(X=1)=2*.04*.96 P(X=<1)=0.9984
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    Graduate Solving Difficult Integral: \int_0^1\ \frac{\arctan(x)}{x(x^2+1)}\ \mbox{d}x

    oops, yes you are right.
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    Graduate Solving Difficult Integral: \int_0^1\ \frac{\arctan(x)}{x(x^2+1)}\ \mbox{d}x

    I am not sure that the integral you linked is related to the problem your friend gave. Where did your friend find it?
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    Finding turning points on a gradient

    Your answer is correct. You are not losing roots. As HallsofIvy stated solving for 0 in this case involves only the numerator because a fraction is equal to 0 iff the numerator is equal to 0.
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    Undergrad How Do I Integrate ln(4x) / 2x?

    f(x)=ln(u) f'(x)=u'/u
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    Graduate Solving Difficult Integral: \int_0^1\ \frac{\arctan(x)}{x(x^2+1)}\ \mbox{d}x

    I am just curious, are you sure that there is a closed form solution to this integral? I have been playing around with it and no matter what substitution I picked I got integrals that are inexpressible in terms of elementary functions (the other substitution combined with change of variable...
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    Finding Covariance with Joint PDF and Distribution Table: How to Solve?

    Ah of course. I usually check that the pdf integrates to 1 over the domain (general case with classroom problems) and it slipped my mind that this may not be a case like that.
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    Undergrad What was Newton's role in the development of Calculus?

    You can also try the wiki entry on Newton
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    Graduate Product Rule for Derivatives of Theta and Time Functions

    I would say product rule looks good.
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    How Is the Value of k Determined in These Function Compositions?

    Your solution looks fine to me. Looks like the key may have made a mistake of not squaring the 3 or something.
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    Discrepancy in Integration of 1/x by Parts

    \int\frac{1}{x}dx=uv -\int vdu= \frac{x+c}{x} - \int \frac{-(x+c)}{x^{2}}dx = etc... u=\frac{1}{x} du=\frac{-1}{x^{2}} dv=1dx v=x+c Please tell me if I am wrong. Regardless, you are looking for the result to be ln|x|+c.
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    Finding Covariance with Joint PDF and Distribution Table: How to Solve?

    Out of curiosity, why would she need to normalize it? From what I understand normalizing would be done to find the correlation matrix.