## STAT 10

(Sec. 5a-5c)

Introduction to Statistical Reasoning

## Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

# Friday, Mar. 01, 2002, turn in after lecture

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

• (HW_5_1) For a two hexagonal die experiment calculate the following probabilities:
• An ace (1+1) occurs at least once in 5 rolls of the two dice.
• A total sum of at least 4, but less than 11 occurs in a single roll of the pair of dice.
• If X is the random variable (R.V.) representing the total sum that turns up. Construct the sample space for a single roll of the pair of dice and the probability table for the R.V. X .

• (HW_5_2) Consider drivers stopped at random for DUI testing. Below is a partially completed probability table providing information about such drivers, with regards to their age (40 or under, and over 40) and whether they were (or were not) wearing seat belts.
•  40 or under Over 40 Total Wearing a seat belt 0.484 ____ 0.853 Not wearing seat belt ____ 0.081 ____ Total ____ ____ 1

•   Complete the table.
•   What is the probability that a driver stopped at random is not wearing a seat belt?
•   If a driver stopped at random is not wearing a seat belt, then what is the probability the driver is over 40?
•   What is the probability that a driver stopped at random is 40 or under?

• (HW_5_3) A single fair tetrahedral (four-face) die is rolled 13 times. What is the probability of getting at least 2 but fewer than 7 aces?

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