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 Jan 16 comment Applications of Residue Theorem in complex analysis? Hello, Welcome to math.SE. IMO one of the main use is to find integrals (i.e, contour integration). It is pretty important for finding real definite integrals also..Search for contour inegration would yielda lot of results. Dec 3 comment Complex solutions of $\sin z = i \alpha \cos z$ put $z_0=i\alpha$ in the final answer.. it also gives you a very important onservation, if $\alpha = 1$ there is no solution. Nov 16 comment What is degree of freedom in statistics? Degree of freedom for a prticle is the number of dimensions only if the motion is not constrained. For an example, consider a particle hanging down from ceiling with the help of a rigid rod, then degree of freedom is less than $3$, right?(it is actually $2$.). Any two independent parameters give all information about the position of particle. (Try to give position using two parameters). If you still have questions, ask. I'll be glad to help if I can.. Nov 15 comment Where does the Chi-square equation come from? IMO chi squared, Student's t distribution, and F distribution, all are from nowhere, they are names given to some functions of random variables which originated during calculations, like in linear regression, ANOVA, etc.They are to some extent derived distributions as opposed to distributions like normal, etc Nov 15 comment simplify natural logarithm nope, you haven't seen real awesome ppl here yet.. welcome again here and have a nice time.. Nov 15 comment simplify natural logarithm putting the values, we get,$\ln 3C = \ln 3$.Take out the log, then we get $3C=3 \iff C=1$. Nov 15 comment simplify natural logarithm if you are satisfied, please consider accepting the answer. meta.math.stackexchange.com/questions/3399/… Nov 15 comment simplify natural logarithm no.. i'll write the answer as it has bypassed the comment stage.. Nov 15 comment simplify natural logarithm Hi, Welcome to math.SE. Please try to use $\LaTeX$ here. If $C$ is a constant, it is better to cancel $\frac 12$ from both sides.. and then use $\ln a - \ln b=\ln \frac ab$ Nov 15 comment Capping part of a sum if I understand meaning of capped spend correctly,(it being maximum amount you can spend on x), then it is nothing but $15 \%$ of total spend. What is the question then?? Please clarify the question.. Nov 15 comment Finding the locus Yes, that was what I meant.. Just wanted him to do this work . :-P Nov 15 comment Why does the distribution of the probability change this way? I don't think your question is clear. What are you asking? Does Bob wants to conduct Testing of Hypothesis for $H_0 : p \sim U(0,1) \text {vs } H_1 : p \sim Beta (3,1)$? (If he does, it might explain the question a little bit.) Please consider editing your question. Nov 15 comment Positive integers less than $N$ not divisible by $4$ or $6$ lol ;-), happened to me a lot of times.. Nov 13 comment What's the proper way for calculating first quartile? math.stackexchange.com/questions/207090/… please check this.. Nov 13 comment Example of a general random variable with finite mean but infinite variance Distribution is defined for $\alpha > 0$ but the question is satisfied for $\alpha \in (1,2]$ as then expectation is finite and variance infinite.., for $\alpha \leq 1$ expectation is infinite, variance doesn't exist.. but Nov 13 comment chi-square distribution: determining the constants c and d Hi, What have you tried? IMO you cannot find such values without using tables.. Nov 11 comment Probability of winning in the lottery Check the comment of Ross Millikan, he did the question assuming you need to get exactly $3$ right. Do similarily for exactly $4$ right and exactly $5$ right. Then you get total no of favourable outcomes. Alternatively, find the complementary probability, i.e getting less than $3$ as that would be easier.. Nov 11 comment Probability of winning in the lottery Hi, welcome to math.SE. Please clarify your question as question is not clear.Like what happens when we guess more than $3$ numbers? Are the rolled numbers different? Thanks. Nov 9 comment Normal Approximation to find probability of stopping at a red light at least 15 times if you are happy with the answer, you can accept it... Nov 9 comment Normal Approximation to find probability of stopping at a red light at least 15 times ok, i'll edit my answer.