## STAT 110 A

(Sec. 3a)
Applied Statistics

## Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

# Friday, Apr. 19, 2002

Please, turn in your homework on the due date. See the HW submission rules. On the front page include the following header.

• (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 resistant measure 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/