3101 Fall 2010
Final Exam
December 10, 2010
Directions:
Write your name and your professor’s name on the cover of your exam booklet. Calculators,
books, notes or any other study aids may NOT be used. Show all work and clearly mark your final
answers.
Answers given as formulas in terms of combinatorial notation will be accepted. Answers that can be
easily simplified should be simplified.
Express all normal probabilities in terms of the distribution
function Φ of the standard normal, i.e. Φ(
x
) =
1
√
2
π
R
x
∞
e

1
2
u
2
du
.
1. (25 points) A computer password of 8 characters is made of 26 letters, 10 digits, and 20 special
symbols on the keyboard of a computer. In how many ways can you form these passwords if
(a) there is no restriction;
(b) there is no digit and all the rest are different;
(c) there are exactly three special symbols;
(d) the first character is a letter, there are exactly two different special symbols and only one
digit.
2. (20 points) There are 3 coins in a box. One is a twoheaded coin; another is a fair coin; and the
third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 SARVER
 Math, Central Limit Theorem, Normal Distribution, Probability theory

Click to edit the document details