Tyler Hilton
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 Apr 28 comment Can we abuse traffic patterns to get home earlier? Interesting stuff. Maybe someone can mathematically quantify this. Apr 12 asked extension of the solution to a nonlinear ODE Apr 7 comment How to find the interest rate? You'd have to isolate for $r$. But that involves taking the 43rd root of some expression. It's not an easy calculation. Most of these textbooks will have tables at the back for precomputed values. Mar 5 revised Congruency proof deleted 120 characters in body Feb 27 comment Computing mean waiting time Look at the definition of expected value. The term inside the summation is "mass point * the probability of the mass point". Jan 4 comment Pseudorandom Number Generator Using Uniform Random Variable This is known as Inverse Transform Sampling. Its a good technique to generate random numbers from a given density, however its naive in a sense that the CDF must be calculated (which is not always possible or is too hard). The proof to why this works is here:en.wikipedia.org/wiki/Inverse_transform_sampling You should look into rejection sampling techniques to see an alternative way to generate random numbers. Dec 31 awarded Nice Question Nov 18 awarded Notable Question Oct 30 awarded Notable Question Oct 12 comment How to solve this limit without L'Hospital's Rule? What have you tried? Sep 26 awarded Notable Question Sep 23 comment Let $f,g\in V^*$ and assume $g \neq 0$. Show that $f= ag$ for some $a \in F$ iff $Ker(g) \subseteq Ker(f)$. What is $V^*$? I am not familiar with this. Sep 20 answered I have two sets that form a function Sep 17 comment Dual Vector Space of linear functionals I am not sure you can define such a thing. Sep 7 comment A quick question regarding hypothesis testing (decision variable) @George I should also note that the answer only applies to interval/real data AND independent groups. If you have interval/real data and have matched pairs, then the test statistics are slightly different. Similarly, If you have two populations and are dealing with nominal/categorical data the test statistics change again. Sep 7 comment A quick question regarding hypothesis testing (decision variable) Yes, when the variances are unknown you use the T test. Remember that choosing the right test statistic requires performing the f-test. To conduct the f-test, the requirement is populations must be normally distributed (and independent). If, indeed, populations are normally distributed, then $n_1, n_2$ doesn't matter. If populations are NOT normally distributed, you'd want your sample sizes $n_1, n_2$ to be large so that you can apply the CLT and thus are able to apply the f-test and continue as above. Sep 7 revised A quick question regarding hypothesis testing (decision variable) added 97 characters in body Sep 7 revised A quick question regarding hypothesis testing (decision variable) added 97 characters in body Sep 7 comment A quick question regarding hypothesis testing (decision variable) I have answered the question here. I am not sure what the etiquette/policy is to copy/paste my answer. Sep 7 answered A quick question regarding hypothesis testing (decision variable)