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  • 0 posts edited
  • 1 helpful flag
  • 27 votes cast
Oct
29
comment Normal Distribution and Cofffee
Hint: you're looking for 3 or more successes (well, failures, but still) in n attempts, where each success has a 1% chance. Use either the binomial distribution (or the normal approximation to it) to find the value of n where the probability is right around 0.5. Other hint: 3 or more successes = the opposite of 0, 1, or 2 successes (might be easier to compute)
Oct
29
comment Elementary matrix proof
Do you mean mu times m if i=l and k=m?
Oct
29
comment Torn between plugging back into the original vs. an intermediate equation…
OK, I think I see what you're asking: if you solve the simpler equation, will all of those solutions still solve the original equation. In this case, they do, but, in general, they might not. In particular, if the simpler equation is itself quadratic (or quartic, etc), the simpler one may give you extraneous roots. So, yes, you need to check that the simpler equations solutions still work with the original equation.
Oct
29
comment Torn between plugging back into the original vs. an intermediate equation…
I prefer plugging into y=3x-1, because you avoid the "extraneous roots" you'd get by plugging into the original.
Oct
29
comment Understanding Mathematical Symbols in Algorithms
I think it means T(i,j)=0 when j<i. I read it as "for all i and j, when j<i".
Oct
27
comment A question about $f(x)\equiv 0$
Derivative of both sides using product rule and fundamental theorem of calculus for right side? We know g'(x) <= 0 everywhere. That, combined with the fact that a negative times a negative is positive MAY (or may not) help.
Oct
27
comment an example of a sequence $(u_n)_n$ taking its values in $[-1,+1]$ such that $(u_{n+1}-u_n)$ converge to zero but $(u_n)_n$ does not converge
If I understand correctly, you're creating a sub-sequence where u(n) bounces between approximately -1 and approximately 1, and thus never converges, is that correct?
Oct
26
comment Is there a difference in the rate of decrease between $f(x)$ and $g(x)$ for increasing $x$?
That's a subjective question, but I would argue "not really", since both functions are O(1/x).
Oct
19
comment Set of numbers which can not be represent as $a_1^n+a_2^n+…a_n^n$
@Antony Ah, OK, so I did misunderstand your question. The solution you give there is for ai=1, which I should've excluded.
Oct
19
answered Set of numbers which can not be represent as $a_1^n+a_2^n+…a_n^n$
Oct
17
comment Coin pair betting paradox
Isn't this the Monty Hall problem in disguise?
Oct
17
comment What are the odds of hitting exactly 100 rolling a fair die
@David Another wording might be "I roll fair 6-sided dice until the total exceeds 100. What is the chance the total was exactly 100 on my penultimate roll?"
Oct
17
comment What are the odds of hitting exactly 100 rolling a fair die
@David Your intuition is good here, but not quite correct. Try working the problem with a total sum of 8 (which appears to be the smallest non-trivial case) and you will see where the bugaboo occurs
Oct
17
comment Suggestion for Math Movies
I can't believe no one's mentioned Story of 1, although it is fairly basic.
Oct
15
comment Trouble understanding case analysis (proof by cases)
Because the square root of 5 is between 2 and 3.
Oct
15
comment How can I prove that (B and (A implies B)) is equivalent to B?
Hmmm... you still need parentheses (and did you just edit your answer after my comment? <G>)
Oct
15
comment How can I prove that (B and (A implies B)) is equivalent to B?
Consider two cases: B is true and B is false. Or, to make things slightly harder, consider these two cases instead: A is true and A is false.
Oct
15
comment How can I prove that (B and (A implies B)) is equivalent to B?
Are you sure about your first step? Don't you have to distribute the first b across the parentheses? I realize you'll just get b V b (which is b), but it looks like you just removed the parentheses, so it's unclear what logic rule you were using.
Oct
8
comment Calculation of $\int_{0}^{\frac{\pi}{4}}\tan^{-1}\sqrt{\frac{\cos 2x }{2 \cos^2 x}}dx$
This doesn't help, but the numerical value is roughly 0.41123351671205660911810379166150629730473746630197, and, according to oldweb.cecm.sfu.ca/cgi-bin/isc/… this doesn't appear to be a "well known" number.
Oct
7
comment Name of a certain set
Perhaps see also math.stackexchange.com/questions/61613/…