Ceng 272 Statistical Computations

Midterm

Apr 02, 2010 10:40 - 12:30

Good Luck!

Answer all the questions.
Midterm

Apr 02, 2010 10:40 - 12:30

Good Luck!

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
- i
- With no restrictions?
- ii
- If each couple is to sit together?
- iii
- If all the men sit together to the right of all the women?

- (20 pts) Define events
- ,
- .

- ,
- ,
- .

- (15 pts) Consider an experiment of rolling a die. Define
and
.
- iv
- Are events and independent?
- v
- What about and ?

- (15 pts) Suppose that and have the following joint probability function:
x 2 4 1 0.10 0.15 y 3 0.20 0.30 5 0.10 0.15 - (a)
- Find the expected value of .
- (b)
- 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
- vi
- a leak in the fuselage (L),
- vii
- malfunctioning oxygen pumb (M),
- viii
- a filter in need of replacement (F).

Cem Ozdogan 2010-04-01