*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:). 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, C, T, G

- A maximum of 4 observations are made, or
- 3
-bases occur in any order, orT- A
TAAtripletappears in this specific order, or(stop codon)- A
occurs on position 2 or 3.GLetbe the random variable (R.V.) representing the total number ofX-bases observed in this composite experiment. Identify theTsample spaceof this experiment and introduce a meaningfulprobability distributionof the random variable. What are theXmeanand thestandard deviationof?X

- (Project
_1_2) For the 8 hrs on campus each week day the average UCLA student randomly meets about 25 acquaintances. Letmeasure 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?X

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