Statistical Methods for Life and Health Sciences
- (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 made, 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?
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Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine