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UCLA Statistics, Neurology, LONI, Math/PIC

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STAT 13 (1a, 1b, 1c)	*Introduction to Statistical Methods for the Life and Health Science*
Department of Statistics	Instructor: Ivo Dinov
Homework 3	Due Date: Friday, Oct. 24, 2003

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.

(HW_3_1) A manufacturer of disk drives for a well-known brand of computers expects 4% of the drives to malfunction during the computers warranty period. Let X be the number of disk drives, in a batch of 10 randomly selected disk drives, which malfunction during this period. X has a Binomial distribution.
- Identify n and p, the parameters of the Binomial random variable.
- In the context of this exercise, state the assumptions required for X to have a Binomial distribution.
- Are the Binomial assumptions satisfied here?
- Calculate the probability that:
1. No disk drive will malfunction during the warranty period.
2. Exactly one disk drive will malfunction during the warranty period.
3. At least two disk drives will malfunction during the warranty period.
4. Between 3 and 6 (inclusive) disk drives will malfunction during the warranty period.

(HW_3_2) Assume the distribution of human blood types in one geographic region is: 30% type A; 11% type B; 49% type O and; 10% type AB. Suppose we select one married couple at random, with the husband and the wife following this blood type distribution.

If the wife has type B blood, what is the probability that the husband has blood type B?
What is the probability that both husband and wife have type A blood?
What is the probability that at least one of them has blood type AB?
What is the probability that they have the same blood type?

(HW_3_3) Members of a health club are classified by gender and number of days per week they exercise. Days per week spent exercising

Gender \ Days of Exercise A(0-1) B(2-3) C(4-5) D(6-7)

Male 40 53 26 6

Female 34 68 37 11

What is the probability that a randomly selected health club member:
- is a female?
- is a female and exercises 4-5 times a week?
- is a male or exercises 4 or more times a week?

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