(HW_2_1) Civil engineer is building a model for deciding whether to place a stop sign or a traffic light on a street intersection. To make this important decision
the engineer sets out to record the traffic events at the intersection. She monitors
the traffic at the intersection until she observes at most 3 traffic events.
Her recommendation on placing a stop sign or lights at the intersection is based on the events she observes. Events are: violations, V, (e.g., illegal crossings) and accidents, A, (e.g., collisions).
Her observation stop also when one of each kind of events occurs (in any order).
Identify the outcomes in the sample space of this experiment and propose
reasonable probabilities for each of those outcomes assuming a violation is twice as
likely as an accident.
Consider the random variable X={number of accidents recorded}. Identify all
possible values for X and calculate their respective probabilities, using your
probability map in part 1. Find the theoretically expected value of the
random variable X, E(X).
(HW_2_2) The Laboratory of Neuro Imaging (LONI) at UCLA has
4 divisions; Anatomy(10), Computational(5), Modeling(20) and Visualization(2),
in parenthesis are the numbers of researchers in each division. Suppose we
are to investigate the personnel's opinions on the recently adopted new administrative
organization in LONI. We decide to poll 10 employees. What sampling
design should be used and how many researchers we need to poll from each
division. Explain.
(HW_2_3) For the following data y={-15, 5, -1, 0, 100, 2, 3, -2, -18, 0, 1, 1, 2}, what is (are) a resistantmeasure of central tendency? Discuss/compute the sample mean, median, 2-times trimmed mean and Windsorized 2-times mean
. Are there other estimates you can identify that may be used for finding
the center of gravity of the data (e.g., (Max-min)/2)?
\Ivo D. Dinov, Ph.D., Departments of Statistics and
Neurology, UCLA School of Medicine/