# Tagged Questions

37 views

### Differentiating Integrals

This problem appears as example 2d of Chapter 5 in "A First Course in Probability - Ross, 8th ed." Suppose that if you are s minutes early for an appointment, then you incur the cost cs, and if you ...
18 views

### Deriving marginal effects in multinomial logit model

For the multinomial logit model, it holds that: $$P[y_i=j]=\frac{\exp{\beta_{0,j} + \beta_1 x_{ij}}}{\sum_h \exp(\beta_{0,h} + \beta_1 x_{ih})}$$. Now my book states that the marginal effect is as ...
31 views

### Gateaux derivative, expected value

Suppose F,G be the distribution functions and \begin{eqnarray*} T(F) & = & \int xdF=E_{F}(x),\\ T(G) & = & \int xdG=E_{G}(x),\\ F_{t} & = & (1-t)F+tG, \end{eqnarray*} How to ...
204 views

86 views

Suppose that we have a multivariate function $f(a,b,c,a_1,b_1)$, where $a,b,c,a_1,b_1$ are all real numbers. $f = \frac{{c({a^2} + {b^2}) + {{({a^2} + {b^2})}^{1/2}}}}{{c{{({a^2} + ... 1answer 101 views ### Trying to understand LMS algorithm This is what's written: So,$h(x)$is basically a linear function to predict values of some training set. I understand everything that's happening up to the point where we take the partial ... 1answer 56 views ### How to derive the equations in 3:19-3:30 provide in a MIT opencourse ware lecture about the least square method? How to derive the equations in 3:19-3:30 provide in a MIT opencourse ware lecture about the least square method? Link: http://www.youtube.com/watch?v=YwZYSTQs-Hk Thanks in advance! 2answers 186 views ### Differentiating the posterior distribution function I am learning about Bayesian statistics and I'm currently doing loss functions. Let$f(\theta | \mathbf{x} ) $be a posterior pdf . Let$F(\theta | \mathbf{x} ) \$ be the associated distribution ...
I am working with the probability likelihood function $$\log \prod\limits_{i=1}^{n} x_i^{y_i} + \log \prod\limits_{i=1}^{n}\left(1-{{x}_{i}}\right)^{n_i-y_i}.$$ I want to take the derivative with ...