TenaliRaman
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 Apr 27 answered Show that $\sin^2 \theta \cdot \cos^2\theta = (1/8)[1 - \cos(4 \theta)]$. Apr 23 awarded Yearling Apr 16 revised Find MLE of $\frac{x+1}{\theta(\theta+1)}e^{\frac{-x}{\theta}}\Bbb I_{(0, \infty)}(x)$ Minor edit to add a detail. Apr 16 comment Find MLE of $\frac{x+1}{\theta(\theta+1)}e^{\frac{-x}{\theta}}\Bbb I_{(0, \infty)}(x)$ I haven't checked your calculations but your steps look right. Apr 13 comment Let. $X \sim \mathcal{U}(0,1)$. Given $X = x$, let $Y \sim \mathcal{U}(0,x)$. How can I calculate $\mathbb{E}(X|Y = y)$? @GrahamKemp You are right, thanks. Apr 12 revised Ratio Inequality latex and some other minor corrections Apr 12 comment Show that $\|\cdot\|_Q$ is a seminorm on $l_{\infty}$ Please use Latex notations in the question so that the question is clearer for the readers. meta.math.stackexchange.com/questions/107/… Apr 12 revised Show that $\|\cdot\|_Q$ is a seminorm on $l_{\infty}$ Latex-ified Apr 12 comment Let. $X \sim \mathcal{U}(0,1)$. Given $X = x$, let $Y \sim \mathcal{U}(0,x)$. How can I calculate $\mathbb{E}(X|Y = y)$? When y = 1, your $\mathbb{E}[X | Y = y] = 0$. That's not right. I am wondering why are you integrating from y to 1, instead of 0 to y for both $f_Y$ and $\mathbb{E}[X|Y = y]$? Apr 11 comment Change of variable in $\int_{-\infty}^{+\infty}\frac{1}{y}\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}y^2}dy$ The function is odd. Apr 9 answered Prove that there are no two functions $f$ and $g$ defined over real numbers that satisfy either of the following functional equations Apr 7 comment Proof that lcm(a,b) = ab/gcd(a,b) math.stackexchange.com/questions/44835/… Apr 6 comment Non-Linear Regression for Parameter Estimation @MathsIsHard I am not sure, what that would entail sorry. However, I found this in matlab [1]. So you don't have to do the silly approximation I suggested, and instead use this to fit your regression parameters. [1] in.mathworks.com/help/stats/nlinfit.html Apr 6 comment Non-Linear Regression for Parameter Estimation One possible approximation is: Assuming Y(s) is always positive. $\log Y(s) = \log K_2 - \theta s - \log s -\log \beta$ where $\beta = \tau^2s^2 + 2\zeta \tau s + 1$. You should be able to use linear regression to find $\theta$ and $\log \beta$. Then solve for $\tau, \zeta$ by setting $\tau^2 s^2 + 2\zeta\tau s + 1 = \beta$. If $Y(s)$ is not positive, then of course this is pointless. Apr 2 comment find $\lim _{t \to \infty}t^3 \left(1-\{f'(t)\}^2 \right)=?$ (+1) Wow, not a problem I would ever think to face in an entrance exam :-) Apr 2 comment find $\lim _{t \to \infty}t^3 \left(1-\{f'(t)\}^2 \right)=?$ Hmm I am getting $t^3(1-\{f'(t)\}^2) = \frac{9t^3(\{f(t)\}^4 - t^4)}{1 + 9\{f(t)\}^4}$. Mar 27 comment Solve for $x$ using the lambert W function $\frac{\ln(1+bx)}{x} = a$ @Dr.MV I am not surprised to hear that on stackexchange :-) Mar 27 comment Solve for $x$ using the lambert W function $\frac{\ln(1+bx)}{x} = a$ @Dr.MV I know right. The moment I posted my answer I felt that my answer got double posted :-D Mar 27 answered Solve for $x$ using the lambert W function $\frac{\ln(1+bx)}{x} = a$ Mar 26 answered Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{1}{4\cos^{2}x + 9\sin^{2}x} dx$