Ivo Dinov
UCLA Statistics, Neurology, LONI
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STAT 13 (1a, 1b, 1c, 1d)

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

## Instructor: Ivo Dinov

Homework 2
Due Date: Wed, April 17, 2013

Please, submit your homework right before lecture on the due date. See the HW submission rules. On the front page include the following header.
• (HW2.1) Suppose that in a certain population of married couples 30% of the husbands smoke, 15% of the wives smoke and in 11% of the couples both the husband and wife smoke. Is the smoking status of the husband independent of that of the wife? Why or why not?
• (HW2.2) A certain drug treatment cures 87% of cases of hookworm in children.  Suppose that 20 children suffering from hookworm are to be treated, and that the children can be regarded as a random sample from the population.  Find the probability that:
• All 20 will be cured.
• All but 1 will be cured.
• Exactly 15 will be cured.
• Exactly 70% will be cured.
• (HW2.3) Childhood lead poisoning is a public health concern in the US. In a certain population, one child in seven has a high blood lead level (>30 µg/dLi). Compute the following probabilities for a randomly chosen group of 10 children from this population:
• P(none have high blood lead)
• P(one has high blood lead)
• P(two have high blood lead)
• P(three or more have high blood lead)

• (HW2.4) Use the SOCR Roulette Experiment to design and run a simulation estimating the probability that a number between 1 and 18  turns up is we spin the Roulette Wheel. Compute the exact probability of this event and list the sample-driven estimates of this event for samples of  size 10, 100 and 1,000. What is your observation about these probability estimates?
• (HW2.5) Suppose that a long stretch of DNA has only Adenine (A), Thymine (T), Cytosine (C) and Guanine (G) randomly occurring with the following probabilities 0.20, 0.3, 0.25, 0.25, respectively. The A, T, C and G nucleotides make up the core of the genetic code for any species. What is the probability that
• A sample of 6 randomly chosen nucleotides contains 5 A's in a row?
• A random sample of 5 nucleotides has equal number of A's and T's?
• Use the SOCR Spinner experiment (remember to set the right number of sectors, 4, and correct probabilities) to simulate the situations above and find empirical answers to the first 2 questions. Run 100 simulations and compare the empirical results of the applet with your theoretical calculations above.

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