Recent content by fireb

Consider AR(1) process \(X_t=bX_{t-1}+e_t\) where \(e_t\) with mean of 0 and variance of \(\sigma^2\) and |b| <1 Let \( a_k \) be a recursive sequence with \( a_1 \) =1 and \( a_{k+1} = a_k + P_k +1\) for \( k = 1, 2 ,...,\) where \(P_k \) is Poisson iid r.v with mean = 1 also, assume \(P_t\)...

Homework Statement Consider X(1)...X(n) IID X~ Poisson(lambda=lnQ), x=0,1,2..., Q >1 Find the Unique MVUE for lnQ? Homework Equations The Attempt at a Solution i let T=sum(x), which is sufficient and lnQ*=sum(x)/n be an unbiased estimator for lnQ Not really sure how to...

Homework Statement Let S be the form of (a, b,c ,d )in R4, given a not equal to 0. Find the basis that is subset of S.Homework Equations The Attempt at a Solution I got a(1,0,0,0), b(0,1,0,0), c(0,0,1,0), d(0,0,0,1) as basis. a not = 0 But i wasn't sure what the significances of a not = to 0...

This seems right. I used w= -2y and got [ 0 1 0 -2] which is essentially the same basis. i guess u used y=-w/2. And ur first base is right

Homework Statement Consider a differentiable curve r: [a,b]-> R(3) such that r(a)= r(b). show that there is a value t belongs [a,b] such that r(t) is orthogonal to r(prime)(t). Homework Equations The Attempt at a Solution My answer: Since r(a)= r(b) the curve must reach a max/min point...

Homework Statement Let x and y have the join probability density function given by f(x,y) = 6 (1-y) 0<= x<=y<= 1 = 0 elsewhere Find P(x<=3/4, y=> 1/2) Homework Equations The Attempt at a Solution I know you have to find the probability in 2 parts...

( I think i got it now... So if we let A(x,y,z) be the closest point from L to R. This condition must be satisfy: RA dot PQ= 0. SO RA = (3-x,-5-y,5-z). And from the dot product, i get x+y-2z=-12. So, i sub in the L into the equation I just got and solve for t, and equal t=-2, yields x=2...

Homework Statement Given p(4,2,3), Q(5,3,1), R(3,-5,5) and let L be a line that passes through P and Q Find the coordinates of that point of the line L which is closest to the point R. Homework Equations The Attempt at a Solution I found the equation of the line L= (x=4+t, y=2+t...

I think i get it, but here is what i got re parametrize the intersection, and i got c=(x=2cost+1,y=2sint, z= 2sint+1) and point (1,2,3) is t=pi/2 and to find radius is R=1/curvature at t=pi/2?

Homework Statement Let C be the curve of intersection of the cylinder x^2-2x+y^2 =3 and the plane z=y+1. Find the radius of the osculating circle of the curve C at point (1,2,3) The Attempt at a Solution I am not really sure how to start it... i tried finding the point of...

Homework Statement The plane that passes through the line of intersection of the plane x-z=1 and y+2z=3 and is perpendicular to the plane x+y-2z=1Homework Equations The Attempt at a Solution I found the intersection point of the 2 planes by setting z=0 yielding the point (1,3,0). Next I found...