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 Apr 9 comment Finding the solution for a (differential) equation involving the pdf and cdf of a normal distribution The website wasn't letting me add comments for a little while. But now it is; I added a bit to my answer above. See if it is useful. Apr 9 revised Finding the solution for a (differential) equation involving the pdf and cdf of a normal distribution added 883 characters in body Apr 9 revised Finding the solution for a (differential) equation involving the pdf and cdf of a normal distribution added 342 characters in body Apr 9 revised Finding the solution for a (differential) equation involving the pdf and cdf of a normal distribution added 342 characters in body Apr 9 answered Finding the solution for a (differential) equation involving the pdf and cdf of a normal distribution Apr 9 revised How to study math to really understand it and have a healthy lifestyle with free time? added 462 characters in body Apr 9 comment How to study math to really understand it and have a healthy lifestyle with free time? I did before even commenting on your answer (link). I'm sorry if my comments offended you. It was merely meant to be constructive, polite criticism. Apr 9 revised How to study math to really understand it and have a healthy lifestyle with free time? edited body Apr 9 comment Moment generating function of two independent variables You can calculate the moments of a random variable by evaluating the appropriate order derivative of the generating function at 0, but I do not think you can obtain the probability directly this way. Also, why are you evaluating at $e^{t}=0$ and not $t=0$? Think about the statement $e^{t}=0$. Maybe that is a typo. For part (a), consider directly calculating the inverse Fourier transform of the product. Apr 9 comment Finding a force function from bodies in equilibrium @Rahul, it would be true for any shapes embedded in a conservative vector field, I think. But you're right that the force field here could be pathological. I have a friend for example who works on molecular sphere packing and I think the force calculations there are pretty hairy. Apr 9 comment How to study math to really understand it and have a healthy lifestyle with free time? Right, but that doesn't help explain how to put time into other things. The poster wouldn't have even asked the question unless he or she already knew that they should put time to these other things. But that's very different than an actual course of action that gives implementational details about how to get one's self to actually commit to this stuff. More relevant advice would be to study the state of the art of self help, things like the procrastination equation or pre-commitment. Apr 9 comment Finding a force function from bodies in equilibrium Think about it. The total force that A applies to B is an average of every point in A affecting every point in B. This can equally well be stated as the effect of an average point in A (i.e. the centroid/center of mass) for each point in B, averaged over all of B. This is why, to great approximation, calculating the force of Newtonian gravity between two bodies only cares about the distance between centers of mass, not the actual distance between every point. I'm sure this could be stated better using language of conservative vector fields. Apr 9 comment Finding a force function from bodies in equilibrium Another thing that comes to mind is that the functional form of the statement that the objects are in equilibrium (force is 0) should reduce to a statement about only the average force exerted by A on B (and vice versa) and the distance between the shapes centroids (or centers of mass if they have density). You should not actually have to integrate over all differential elements of both bodies. Apr 9 comment How to study math to really understand it and have a healthy lifestyle with free time? I'm not trying to be rude or anything, but often it does not help t simply say an imperative like "schedule time for exercise." Usually people are asking how to schedule such time. Apr 8 revised How to study math to really understand it and have a healthy lifestyle with free time? added 2434 characters in body Apr 8 revised How to study math to really understand it and have a healthy lifestyle with free time? added 2434 characters in body Apr 8 revised How to study math to really understand it and have a healthy lifestyle with free time? added 2434 characters in body Apr 8 answered How to study math to really understand it and have a healthy lifestyle with free time? Apr 8 answered Math Database For Problem Descriptions In An App. Apr 6 comment Finding a force function from bodies in equilibrium For the numerical approximation part, this sounds like a problem that will benefit from simulated annealing.