Recent content by tennishaha

In the least square linear regression, say we have y=Xb+e (y,b,e are vector and X is matrix, y is observations, b is coefficient, e is error term) so we need to minimize e'e=(y-Xb)'(y-Xb)=y'y-y'Xb-b'X'y+b'X'Xb we can take the derivative of e'e to b, and we can get the answer is 0-2X'y+2X'Xb...

I think the ball should be still relative to the ground after hitting the wall (velocity=0). Am I correct?

I think it should be a reflection kind of problem. Before hitting, the velocity is u, and after hitting the velocity should be -u(same magnitude, but opposite direction), but I am not sure the u here is relative to ground or relative to the wall. Any ideas?

Homework Statement A very heavy wall moving at 60mph, a ball moving same direction at 120 mph. What is direction and speed of ball after ball hit wall. Homework Equations I am thinking to use the momentum conservation: mass of ball*velocity of ball+mass of wall*velocity of wall don't...

Your one can be shown using the jacobian J=|a b| =ae-bd d e then the joint pdf of y1 and y2= joing pdf of X1 and X2 / (ae-bd) X1 and X2 are independent, you can easily get their joint pdf, and you can get joint pdf of y1 and y2, it is also a joint normal

The attached equation is from http://en.wikipedia.org/wiki/Multivariate_normal_distribution can anyone show me why the conditional variance is equal to (1-rou^2)* variance of y thanks

thanks! :) yes, it should be this

http://en.wikipedia.org/wiki/Girsanov_theorem Could anyone tell me what does the [] of [X]t mean in the attached equation, shown in wiki's Girsanov_theorem page? Thanks

Homework Statement v is a vector with norm(v)<1 what is the inverse of (I+vv') where I is a identity matrix Homework Equations The Attempt at a Solution

Homework Statement How to integral this one? 1/(1+a*cosx) Homework Equations The Attempt at a Solution

Homework Statement y''+y'+y=0 Homework Equations say we get the roots: -1/2+i*sqrt(3)/2 and -1/2-i*sqrt(3)/2 The Attempt at a Solution I saw two solutions to this problem first is y=e^(-1/2*x)(c1*cos(sqrt(3)/2*x)+c2*sin(sqrt(3)/2*x)) second is...

for a brownian motion W(t) W(t_i+1)-W(t_i) is normal distribution with mean 0 and variance t_i+1-t_i so this means var(W(t_i+1)-W(t_i))=var(W(t_i+1))-var(W(t_i))=t_i+1-t_i I don't think the above equation satisfies because W(t_i+1) and W(t_i) are not independent. Any comment? thanks

52 cards, 13 values (A to K) and 4 suits. what's the probability of getting 5 cards with a four-of-a-kind (same value)? My solution: first card 52/52, second 3/51, third 2/50. fourth 1/49, fifth 48/48 so (52/52)*(3/51)*(2/50)*(1/49)*(48/48)~4.8e-5 The solution provided by the book 13x48/(C 52...

1. If X is uniform distributed in (0,pi), what is E(X|sinX)? 2. Suppose X and Y are Gaussian random variables N(0,sigma_x) and N(0,sigma_y). what is the distribution of E(X-Y|2X-Y) Can anyone help? thanks

In the attached equations, for the second last step to the last step why dSdS=sigma2S2dt ?