Mr. F
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 Apr9 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. Apr9 revised How to study math to really understand it and have a healthy lifestyle with free time? edited body Apr9 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. Apr9 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. Apr9 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. Apr9 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. Apr9 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. Apr9 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. Apr8 revised How to study math to really understand it and have a healthy lifestyle with free time? added 2434 characters in body Apr8 revised How to study math to really understand it and have a healthy lifestyle with free time? added 2434 characters in body Apr8 revised How to study math to really understand it and have a healthy lifestyle with free time? added 2434 characters in body Apr8 answered How to study math to really understand it and have a healthy lifestyle with free time? Apr8 answered Math Database For Problem Descriptions In An App. Apr6 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. Apr6 comment What matrices preserve the $L_1$ norm for positive, unit norm vectors? Another way to put it is that the columns of $P$ are discrete distributions. Multiplying such a matrix by another distribution will yield a mixture of the columns, where the mixture weights sum to 1, hence that mixture must also be a discrete distribution. Apr5 answered Probability of absorption in a discrete Markov chain Apr5 comment Find the Bayes estimate of $θ$ That's almost correct, but what would happen if $\theta$ was smaller than 5? Could you ever draw a 5 from such a uniform distribution? Also, instead of just looking for the "peak" as I wrote, it sounds like you need the mean squared error. First work on getting to the point where you are confidence that you understand $p(\theta|5)$ then we can use the definition of mean squared error to finish off the problem. Apr5 comment Find the Bayes estimate of $θ$ What have you tried? Here is a hint: what is the probability $P(5|\theta)$ since you know that the probability of an observation is uniform between $0$ and $\theta$? Once you know this, then you can write down $P(\theta | 5)$ using Bayes' rule and find where it has a peak. Apr4 revised What is a “vanishing moment”? added 259 characters in body Apr4 answered What is a “vanishing moment”?