STAT 251 / OBEE 216

Statistical Methods for Life and Health Sciences

Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology

http://www.stat.ucla.edu/~dinov/

PROJECT 1

Due Date:

Monday, Jan. 28, 2002, turn in after lecture

See the HW submission rules . On the front page include the following header .

(Project_1_1) Suppose a scientific experiment (e.g., reading DNA sequences) has exactly 4 possible outcomes (encoded by: A, C, T, G). Assume all 4 possible outcomes are independent and equally likely at each observation. A composite experiment is carried out until one of the following stopping criteria occurs:

A maximum of 4 observations are carried, or

3 T-bases occur in any order, or

A TAA triplet (stop codon) appears in this specific order, or

A G occurs on position 2 or 3.

Let X be the random variable (R.V.) representing the total number of T-bases observed in this composite experiment. Identify the sample space of this experiment and introduce a meaningful probability distribution of the random variable X . What are the mean and the standard deviation of X ?

(Project_1_2) For the 8 hrs on campus each week day the average UCLA student randomly meets about 25 acquaintances. Let X measure the time that passes until the first acquaintance is met. What is (an approximation to) the probability that the first acquaintance is met after the 1-st but before the 3-rd hour a student spends on campus? What is the mean time for meeting the first acquaintance?

\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine/