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 Mar 22 comment Find the closed formula for following problem. 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?