# André Nicolas

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 22h answered Partitions of a set into three parts 22h comment Sets of integers in the form $a^2 + 4ab + b^2$ As an unhelpful comment (as usual I cannot find it) essentially the same question has been asked and answered on MSE, no more than $2$ weeks ago. 22h revised Deck of cards probability added 125 characters in body 22h comment Degree of $x^{4}-4$ over $\mathbb{Q}$ and $\mathbb{Z}/5 \mathbb{Z}$ The degree of $\mathbb{Q}(\sqrt{2},i)$ over $\mathbb{Q}(\sqrt{2}$ is not $1$. The polynomial $x-i$ does not have coefficients in $\mathbb{Q}(\sqrt{2})$. 22h answered Deck of cards probability 22h answered What does it mean for a solution to a Linear DE to be homogeneous? 23h comment Integral help needed If we use the Cauchy Principal Value, it will be OK. But that is not the default interpretation. 23h comment Integral help needed There is a typo in the problem, or a serious error. The integral does not exist. 23h comment Unbiased estimators in an exponential distribution In almost all situations you will be right. The way most courses are organized, the exponential distribution would have been discussed before one talks about estimators. 1d comment Unbiased estimators in an exponential distribution Calculate $\int_0^\infty \frac{y}{\theta}e^{-y/\theta}\,dy$. (Use integration by parts.) That is the only integral calculation that you will need to do for the entire problem. 1d comment Limit of 2 functions equal to 0 at x equal to zero If we know $f'(0)$, then we can sort of cheat and use the definition of the derivative. 1d revised Consider throwing two six-sided dice. Let X be the sum of the two values and let Y be the product of the two values. added 116 characters in body 1d answered Consider throwing two six-sided dice. Let X be the sum of the two values and let Y be the product of the two values. 1d revised Double Angle Formula? deleted 37 characters in body 1d comment the sum of the first n odd integers squared proof @Oleg567: Amusingly enough, worked examples of induction usually do not do it in your "best" way. Such worked examples make things unnecessarily mysterious. 1d comment the sum of the first n odd integers squared proof The base case is $n=0$. 1d comment Help with proof question? The proof depends on what properties of parallel lines, triangles have already been proved in your course, or are take for granted. One way is that by properties of parallel lines, $\angle ABC=y$. Then by a property of external angles of a triangle, $x=z+y$. There are many other ways. 1d comment Probability of selecting odd number of black cards. Sure, conditional probabilities are changeable. 1d comment Determine the centre, radius and interval of convergence of the power series Ratio Test and Root Test will both work nicely. If the $x$'s are real, to deal with $x=\pm 1$ use Comparison. 1d revised Probabilty & Statistics Problem deleted 6 characters in body