Quiz #1 1.5 hours - open books and notes
Problem 1 (25 points) A device has a sensor connected to an alarming system. The sensor triggers with probability 0.95 if dangerous conditions exist in a given day and with probability 0.005 if conditions are norma

Quiz # 2
In-class, open books and notes
Problem 1 (40 Points)
An environmental variable X has value Xi in day i. Due to budgetary constraints, X is
measured only every third day. If X is measured in day i, then the observed value of X i
1
is used to estim

Homework Set #10
Problem 1
Suppose that hurricanes occur according to a Poisson Point Process with unknown parameter . Given that 5 hurricanes occurred during a two-month period, estimate by: (a) The Method of Moments (b) The Method of Maximum Likelihood,

Homework Set #9
The pressure acting on the windows of a high-rise building is Y = CV2, where V is wind
speed in km/hr, and C is a local effect factor, the units of which are such that Y is in
kg/cm2.
The local effect factor and the 10-year peak wind speed

Homework Set #8
A plain concrete column is subjected to a random axial load W with lognormal distribution, mean value m W = 3000 kN [kN = Kilo Newton, a unit of force] and coefficient of variation VW = 0.2 . The resulting compressive stress is given by W

Homework Set #7
Problem 1
Consider a sequence of random variables X1, X2, , Xi, , for example denoting the
monthly profits of a supermarket chain. Suppose that Xi ~ (m,2) for all i and that the
correlation coefficient between Xi and Xj, ij, depends only o

Homework Set #6
Problem 1
In planning a building, the number of elevators is chosen on the basis of balancing initial
costs versus the expected delay times of the users. These delays are closely related to the
number of stops the elevator makes on a trip.

Homework Set #5
Problem 1
X has probability density function as shown below.
fX ( x )
2
2 x , 0 x 1
f X (x) =
otherwise
0,
0
1
X
Calculate the mean value m X , variance 2 and second initial moment E[X 2 ] . Verify
X
the relaton E[X 2 ] = m 2 + 2 .
X
X
Pr

Homework Set #4
Problem 1
Suppose that buses arrive at a terminal according to a Poisson Point Process with mean
rate = 1 /(15 min) . Simulate the Poisson Point Process of bus arrivals over a period of
10,000 minutes using the procedure discussed in class

Homework Set #3
Problem 1 Read Application Example 8 and do Problem 8.1. Problem 2 The way MIT admits undergraduate students is exemplified in the following table. Each applicant is rated to a discrete "scholastic index" X (horizontal axis) and a discrete

Homework Set #2
Problem 1
A machine to detect improper welds in a fabricating shop detects 80 percent of all
improper welds, but it also incorrectly indicates an improper weld on 5 percent of all
satisfactory welds. Past experience indicates that 10 perce

Homework Set #1
Problem 1
Suppose that the occurrences of earthquakes and high winds are unrelated. Also suppose
that, at a particular location, the probability of a "high" wind occurring in any single minute
is 10-5 and the probability of a "moderate" ea