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~IEO 4150 SECOND EXAMINATION NOVEMBER 11, 2008
SHOW ALL, WORK! !
1. This exercise refers to the table provided, showing education and related
data for the states. Using the circled population data for the Mountain and
Pacific states (AK, AZ, CA
C1403 Midterm 1 Formula Sheet
x(t ) xm cos(t 0 ) v(t ) xm sin(t 0 )
a(t ) 2 xm cos(t 0 ) 2 x(t ) 1 f 2f T k m T 2 m k 1 2 U (t ) kxm cos 2 (t 0 ) 2 1 2 K (t ) kxm sin 2 (t 0 ) 2 1 2 E mec U K kxm 2 I T 2
1 2 v 2 ym 2 2 y 1 2 y x 2 v 2 t 2 y( x, t )
SIEO 3600: HMWK 6
You will find the Lecture Notes 5 (Further Topics in Probability) posted on our course
website very useful for doing this HMWK assignment.
1. Let X have an exponential distribution at rate ; its probability density function
is f (x) = ex
IEOR 3600: Solutions to HMWK 1
f (u)du = 1 ex and
f (x)dx = limx 1 ex = 1.
(b) 0 xf (x)dx. Integration by parts (U = x,
dV = f (x)dx) easily yields the answer as 1/.
(c) 0 x2 f (x)dx. Integration by parts twice yields
the answer as 2/2 .
IEOR 3600, HMWK 2, Professor Sigman
Recall that there are several notations used in books to denote the complement of a
set. For a set A , all three of these denote the complement of A: A, A0 , Ac . The
complement is defined by cfw_w : w
/ A. (In our cla
IEOR 3600: HMWK 4
1. A company makes boxes of various sizes as follows: The length (L) is a rv with
probability mass function P (L = 2) = 0.3, P (L = 4) = 0.7. The width (W) is
a rv with probability mass function P (W = 3) = 0.3, P (W = 4) = 0.4, P (W =
IEOR 3600: HMWK 3
1. Suppose that apriori we do not know the proportion p of voters who will vote for
candidate A (versus candidate B), but that when we randomly selected five voters,
exactly 3 said they would vote for A. Find the value of p that maximize
-e). d .r
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APMA4901: Seminar in Applied Mathematics Wednesdays 11:00am-11:50am prof: Chris Wiggins [email protected] c Chris Wiggins 2011. Please do not duplicate without permission. The seminar in applied mathematics is a required course for all juniors an