9. Photographs taken from space show that Earth is striking in its beauty. Blue oceans cover nearly threefourths of the surface, broken by the continental land masses and scattered islands. The polar caps are
white with snow and ice, and white clouds are
Test on Model 1:
Null hypothesis: the regression parameters are zero for the variables
ABSLATIT, AVELF, BRIT, CIV72, DPOP6090, ECORG, ENGFRAC, GDE1,
REFERENCES FOR DATA SOURCES:
Barro, R.J. 1999. Determinants of Democracy. Journal of Political Economy 107(6), pt 2: S15883.
Barro, R.J. mimeo.
Barro, R.J. and J.W. Lee. 1993. International Comparisons of Educational Attainment. Journal
of Monetary Econom
We know from the text (Theorem 5.7.17) that from a chordal graph we can always
produce a junction tree. In fact the algorithm is quite simple. Given a chordal graph find
all the maximal cliques. Then create a fully connected graph over the cli
First, we note that the edge cliques are maximal. We assume decomposability. First we
associate an empirical marginal with each clique and then for every intersection we
divide out the empirical marginal of the intersection from one of the par
138 THE HDO FlLTER
11.14 Generate the time-varying solution to Pk for Problem 11.? with P0 = 1.
\Nhat is the largest value of 6 for which Equation (11.90) will be satisﬁed for all k
up to and including it = 20? Answer to the nearest 0.0
130 THE HQC FILTER
where Q I diag(q,0), and q is the variance of wk. Multiplying out this
equation and equating the elements on both sides gives
(P11 + P12)“ — 1312/3)
1 + Pll/R
*(P11 + P12)P12/R
P12 — Fizz/R
134 THE Hac FlLTER
This is true for 6 S 1.25 and 6 2 3.25. Another condition for the existence of
the H00 ﬁlter is that Equation (11.90) must be satisﬁed.
P’l — as. + Hfsglnk > 0
P‘1 i 6 + 1 > 0
This is always true if 6 < 1. If 6 > 1 then this inequality
132 THE Hcc FILTER
Setting these partial derivatives equal to zero and solving gives
1'1 = 4
2:2 = 0
3:3 : 4
A = —8
11.6 Maximize (142: —— $2 + 6y i y2 + 7) subject to the constraints + y 5 2)
and (a: + 2y S 3) [Lue84].
One of four situations ho
124 ADDlTlONAL TOPICS IN KALMAN FiLTERiNG
where f 2 0.8, and wk is zero-mean white noise with a variance of 0.01. We measure
the tread height every 7 weeks with zero-mean white measurement noise that has
a variance of 0.01. The initial tread height is kno
128 THE Hog FILTER
So we see that (I + ATIA 2 AU + Ari.
11.2 Consider a scalar system with F = H = 1 and with process noise and
measurement noise variances Q and R. Suppose a state estimator of the form
is used to estimate the state, whe
136 THE am FILTER
The steady-state a pastem'om‘ Kalman ﬁlter Riccati equation solution is obtained
from Equation (5.19) as
P+ : [(P‘)_1 + HTH]_1
where P“ is the steadyrstat—e a priori Kalman ﬁlter Riccati equation solution, and
we have substitut
ADDITIONAL TOPICS IN KALMAN FILTERING
Pmy(k, k A 1) is found as
[P(k) A PmUc, k —1)]FT(k — 1, MHT
130‘ch — 1) is found as
Pmy(k,k — 1)
PUc, k — 1) = PUc) — 33903,}: e1)3*1(k —1)Pg;(k,k ~ 1)
_ 1/3 0
_ 0 1
c). In part (b) we saw that P‘Uc) = I
12D ADDITIONAL TOPICS IN KALMAN FILTERING
Where all quantities are deﬁned at time k. The second expression can be derived as
P9 = Elly - ﬁlly - @lTl
= E[(H:c+ v w ch')(Ha:+v — HijT]
: HEW: — we: — :E‘)T]HT + HEKJ: — sniff] + Ewe i 52-)T1HT + E(va
126 ADD‘TIONAL TOPICS IN KALMAN FILTERING
r. L, _ _‘ _ w 7 _ .
3 ‘ V
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Figure 10.2 Solution to Probiem 10.16 CHAPTER 11
The H00 filter
11.1 Show that. (I + A)‘1.4 : AU + Ari.
(b) H: X c = X p A: X c < X p
(c) H: pc = pp A: pc < pp A: c < p
(d) H: X c = X p A: X c 6= X p
Past performance 1998 Dec - 95%
45. Refer to the JMP output above. Which is correct?
(a) We are about 95% confident that the rats in the poisoned g
37. Calculate the observed value of the test statistic for the test of H0 : 1
2 = 0 versus Ha : 1 2 < 0 on the basis of the following information.
Test the hypotheses at the 5% level of significance.
Sample statistics for group 1:
EATS 1011 3.0 Introduction to Atmospheric Science
e. 10 m
21) What would the earth's surface temperature be if there was only N2 and O2 and no
radiatively active gases, such as H2O and CO2 in the atmosphere and the albedo
was the same as now? (Select from
(a) H: 1 2 =0 A: 1 2 6= 0
(b) H: X 1 X 2 =0 A: X 1 X 2 < 0
(c) H: 1 2 =0 A: 1 2 < 0
(d) H: X 1 X 2 =0 A: X 1 X 2 > 0
(e) H: 1 2 =0 A: 1 2 < 0.
27. The test statistic, rejection region (=.05), and the p-value are:
(a) T =1.2173; reject if T 1.7
(e) H: 1 2 = 0 A: 1 2 > 0
Past performance 1990 Feb - 97%
31. The value of the proper test statistic and rejection region (= 0.05) are:
(a) T = 1.38; reject H if T > 1.71
(b) T = 1.26; reject H if T > 1.75
(c) T = 1.38; reject H if T > 2.14
Past performance 2006 Dec - 87%
48. A Type I (false positive) error would occur if:
(a) We conclude that larger nests have the same size eggs (on average)
when in fact they are larger.
(b) We conclude that larger nests have larger eggs (on ave
(a) 1.896, 0.033
(b) 1.896, 0.131
(c) 1.896, 0.065
(d) 1.887, 0.059
(e) 1.887, 0.118
Past performance 1993 Feb - 38% (a-53%)
41. A Type II error would occur if:
(a) We conclude malathion is ineffective when in fact it was effective.
(b) We con
1. Most recordings made in New Orleans were recorded at this famous studio.
A. Floyd Soileau's Ville Platte Studios
B. Jay Miller's M&S Studios
C. Sam Phillips' Memphis Recording Service
D. Cosimo Matassa's J&M Studios
Points Earned: 4/4
Correct Answer: D
Page 10 of 16
(d) What is the pOH at the halfway point (or midpoint)?
pOH = 4.74
(e) Use the value in (d) to calculate the pH.
pH = 9.26
(f) What volume of acid is needed to reach the stoichiometric point in the titration i.e. when the