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 Yearling
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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 $\int_{0}^{\frac{\pi}{2}} \frac{1}{4\cos^{2}x + 9\sin^{2}x} dx$