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Mar
22
comment Find the closed formula for following problem.
See also stackoverflow.com/questions/4455575/…
Mar
22
comment List step by step instructions to turn a properly colored pie of j sectors into a properly colored pie of j+1 sectors
I think these are two separate problems. Creating a 5-slice pie from a 4-slice pie is different than counting all possible 5-slice pies. I don't think you need recursion to compute the number of ways to color an n-slice pie, even though b) sort of suggests you do.
Mar
20
answered Probability of inequalities between max values of samples from two different distributions
Mar
19
comment Simple Nonlinear Differential Equation
wolframalpha.com/input/?i=y%27[x]+%3D+y[x]^2+%2B+x^2 is the solution in the general case, not sure it works for y(0)=0 though.
Mar
18
comment Probability of inequalities between max values of samples from two different distributions
Are you familiar with Mathematica's "ExtremeValueDistribution"?
Mar
17
comment Probability of inequalities between max values of samples from two different distributions
I'm working on this and got an approximate answer of about .9515 for your specific case. Is this close to what you're getting?
Mar
17
comment Expected value for maximum of n normal random variable
Probably unhelpful, but the median of this distribution is $\sqrt{2} \text{erf}^{-1}\left(2^{\frac{n-1}{n}}-1\right)$
Mar
17
comment Generalize finding perfect squares by adding odd numbers
mathforum.org/library/drmath/view/56953.html may or may not be helpful. Searching for "finite differences" and "polynomials" may also help. Also, I might be missing something, but didn't you just show that you can start with k! and work your way up by adding adjacent terms?
Mar
17
comment Probability of inequalities between max values of samples from two different distributions
sjsu.edu/faculty/watkins/unboundedmax.htm may be helpful. @Vossler uses those formulas below, but I had to think about them for a second: the chance that the max of n samples is x is the chance that n-1 samples are < x and 1 sample equals x. To find this, we integrate CDF^(n-1)(x) * PDF(x), as Vossler does below.
Mar
17
comment Binomial distribution question Holiday resort overbooking
I meant, show how you computed P(X=n) for example.
Mar
16
comment Binomial distribution question Holiday resort overbooking
Two thoughts: 1) have you considered using the normal approximation to the binomial distribution? 2) how exactly did you compute P(X=0) + P(X=1)+...+P(X=Z) in the first method?
Mar
16
comment Probability of inequalities between max values of samples from two different distributions
Hint: consider the problem in the other direction. Suppose you drew a random sample of 25 citizens from country B. What would the sample standard deviation have to be for you to estimate the total deviation as 3 inches? How does the standard deviation of a sample compare to the standard deviation of the population, given a number of samples n?
Mar
16
comment Find a function which has same integrals as another function
My first thought would be to try something like integration by parts to simplify the integrals.
Mar
16
comment Determine age of Charcoal from Current Decay Rate? (Differential Equations)
Hint: use the 6.68 ... how long has the living wood decayed?
Mar
16
comment Generalize finding perfect squares by adding odd numbers
You're talking about finite differences here, and the continuous analog is derivatives. And the kth derivative of n^k is ... ?
Mar
16
comment lawn sprinkler differentiation problem
Agree with @Dr.MV -- if v is the water speed, it should be constant in this problem, no?
Mar
16
comment Three Altitudes of a triangle are concurrent
This doesn't help you, but you could do this just using formulas if you were allowed.
Mar
16
comment Construct a regular expression for a given language
I don't think this can be done. In some sense, you're trying to count the total occurrences of a letter in an arbitrarily long string with other letters.
Mar
16
revised Earth population growth rate is exponential or logarithmic?
population growth models
Mar
16
answered Earth population growth rate is exponential or logarithmic?