Michael Hardy
Reputation
144,431
399/400 score
 11h revised Confidence interval of a random variable for an ordinary linear regression \cdot and \|\| 11h revised I need help with doing two inductive proofs using integration by parts. added 1 character in body 11h reviewed Approve Find 2 continuous functions $F$ and $G$ defined on $[a;b]$, such that $F'(x) = G'(x)$, but $F(x) - G(x) \neq \text{const}$ 12h comment I need help with doing two inductive proofs using integration by parts. @user190080 : If you want to clean up the MathJax usage, then the following isn't a really great place to leave it: $\int_0^{pi/2} \sin^{2n - 1}(x)dx = \frac{2*4*6***2n}{3*5*7***(2n + 1)}$. I changed it to this: $$\int_0^{pi/2} \sin^{2n - 1}x \, dx = \frac{2\cdot4\cdot6\cdots2n}{3\cdot5\cdot7\cdots(2n + 1)}$$ Note $\pi$ rather than $pi$ and $\text{“}\cdots\text{''}$ rather than $\text{“}***\text{''}$. Using an asterisk in this context is for situations when you're limited to the characters on the keyboard. You can write $4\cdot5$ or $4\times5$; there's no need for $4*5$. $\qquad$ 12h revised I need help with doing two inductive proofs using integration by parts. added 52 characters in body 12h revised I need help with doing two inductive proofs using integration by parts. added 29 characters in body 14h revised In $\mathbb C^2$, Show that $\langle x,y\rangle=xAy*$ is an inner product. added 6 characters in body; edited title 14h revised Explicit functions evaluated added 1 character in body 14h comment Properties of the solution of a linear system with random equations Are the $x_i$ independent of each other, and likewise the $y_i$, and are $x_i$ independent of $y_i$? You're omitting information. $\qquad$ 14h comment Properties of the solution of a linear system with random equations Are you asking about properties of least-squares estimates of $\alpha$ and $\beta$, rather than about $\alpha$ and $\beta$ themselves? $\qquad$ 14h revised Properties of the solution of a linear system with random equations added 30 characters in body 14h revised If $\{a_k\} \in \ell^2$, how to prove $\sum a_k/k$ converges absolutely. deleted 9 characters in body; edited title 15h revised Equation of the geodesic corresponding to the metric $ds^2=du^2+f^2(u)\,dv^2$ added 5 characters in body; edited title 15h answered Prove $2^{X \cap Y \cap Z} = 2^X \cap 2^Y \cap 2^Z$ for any three sets $X, Y, Z$ 16h comment Why do we like sticking random variables into their own distributions? It is reasonable to cal $f(s)\,ds$ a distribution. The function $s\mapsto f(s)$ is the density function of that distribution with respect to the measure $ds$. $\qquad$ 16h comment Is there a way to do that integration? Please observe proper MathJax coding as in my edits to this answer. Writing a\cos b or a\cos(b) results in proper spacing, thus: $a\cos b,\quad a\cos(b)$. $\qquad$ 16h revised Is there a way to do that integration? added 4 characters in body 16h revised Is there a way to do that integration? added 10 characters in body 16h revised Characterization of Groebner Bases in terms of unicity of remainders added 27 characters in body 16h revised Tangent plane of a surface at points with given gradient added 1 character in body