Ceng 272 Statistical Computations
Answer all the questions.
Apr 02, 2010 10:40 - 12:30
Write the solutions explicitly and use the statistical terminology
- (5 pts) How many distinct words can be formed using all the letters of the eleven-letter word MISSISSIPPI?
- (10 pts) Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated
- With no restrictions?
- If each couple is to sit together?
- If all the men sit together to the right of all the women?
- (20 pts) Define events
Among elderly people who are 70 years of age, suppose we have
What is ?
- (15 pts) Consider an experiment of rolling a die. Define
- Are events and independent?
- What about and ?
- (15 pts) Suppose that and have the following joint probability function:
- Find the expected value of .
- Find and .
- (20 pts) An electrical firm manufactures a 100-watt light bulb, which, according to specifications written on the package, has a mean life of 900 hours with a standard deviation of 50 hours. At most, what percentage of the bulbs fail to last even 1100 hours? Assume that the distribution is symmetric about the mean. (Hint: Use Chebyshev's theorem)
- (20 pts) Astronauts on the space shuttle realize that oxygen level is dropping (event, ). There are 3 possible problems that can cause oxygen levels to drop
The astronauts know that , and . Ground crew runs simulations to find , , . What should the astronauts try to fix first?
- a leak in the fuselage (L),
- malfunctioning oxygen pumb (M),
- a filter in need of replacement (F).