Assignment2
ED13B013 (Sai Bhargava Ramu)
9 September 2016
1.
a)
Given an AR(1) process v[k] = 1 v[k 1] + e[k] and we know
E(v[k]v[k l]) E(v[k])E(v[k l])
p
var(v[k])var(v[k l])
(
e2 l = 0
e[l] =
0
else
corr(v[k], v[k l]) =
Pl1
But we know v[k] = l1 v[k l]

Assignment5
ED13B013 (Sai Bhargava Ramu)
14 November 2016
1.
a)
y = X +
Least square residuals are
e = M
ee0 = 0 M
E(e0 e|X) = E(0 M |X)
As tr(0 M ) is a 1x1 matrix
tr(E(e0 e|X) = tr(E(0 M |X)
SSE = tr(M E(0 |X)
SSE = e 2 (tr(I X(X 0 X)1 X 0 )
SSE = e 2

Assignment4
ED13B013 (Sai Bhargava Ramu)
22 October 2016
1.
By resolving psd we know it is AR(1) process , v[k] = 0.4v[k 1] + 1.2e[k]
( 2
e
l=0
[l] = 1d2 l
| d | else
ACVF calculated are 1.714,0.685,0.274,0.109 . . . .
Formulation in R
f<-function(x)cfw_1

CH5350 ASSIGNMENT-1
ED13B013
1.
a)
Arrivial times are exponential distribution
f (x) = e-x
1
E(x) = 0 x e-x x =
(i) Since =4 per hour
E(x)=15 min per bus
When reached at 7:50 AM next bus would be at or before 8:05 AM
(ii) If last bus departed at 7:45 AM