1. For this, you want to use the BCR. Order counts here since we are dealing with words. Note the
There are 5 ways to pick a vowel.
There are 4 spaces to put that vowel in.
There are (21)3 ways to pick 3 distinct consonant
How many 4-letter words can you form if no letter is used twice
and each word must contain exactly one vowel (A, E, I , O or U)?.
Suppose there are N people in the class and that I randomly pass
back the rst exam. a) What is the probabil
MA581 Practice problems Solutions
Problem 1 The sample space is all groups of 3 people from the oce. Every group of 3 people in the
oce has an equally likely chance of getting picked, so the size of our sample space is | = 16 . For both
a) and b), the s
The least squareslinej} = n + ,911 is the line that has the following two properties:
1. The sum of the errors equals 0, i.e.,mean error of prediction : 0.
L The sum of squared errors (SSE) is smaller than that for anyI other straight-
CAS MA 581
Work problems; problems are weighted uniformly, as are subdivisions within a problem.
Justify your solutions as indicated in lecture for fullest credit.
Suppose the probability that it takes you exa
Intervals for Real Numbers
( a , b ) =cfw_ x R :a< x< b
[ a , b ] = cfw_ x R :a x b
():bounded open interval
:bounded closed interval
( A B) = A B
from the m
(m)r or mPr .
If P ( B| A )=P( B)
P ( A B
Discrete Random Variables and
From Variables to Random Variables
5.1 The answers will vary. One such example is the variable that measures time until arrival of
next customer to, say, a given bookstor
CAS MA 581
MA225 or MA230 (or equivalent: multivariate calculus)
Dan Weiner and TA
Room 246 MCS Building, 111 Cummington Street
617-353-9546, [email protected]
Office Hours: Wed &
MA581 Fall 2015
Instructor: Prof. Murad Taqqu, MCS 252, Tel 617-353-3022. Email: [email protected]
T ime and place: M ,Wd, F 11-12, CAS 224.
U pdated inf ormation on blackboard
T extbook: Neil A. Weiss, A Course in Probability. Pearson: Addiso
Discrete distribution problems
1. Bill and Ted play a best-of-5 game series of rock-paper-scissors.
Since Bill trains in the US Rock-Paper-Scissors League, he has a 0.6
probability of winning each individual game. What is the probability
that Bill wins th
Probability Practice Problems
Using concepts from this class, compute the following integrals. (tricks like u-substitution, integration by
parts, etc. wont work)
x1/2 ex dx
Let X and Y be independent Poisson random var
MA581 Practice problems
Jim and Pam enter a rae where 3 dierent people from their oce are randomly selected to win a free trip.
There are 16 people total in their oce.
a) What is the probability that both Jim and Pam are selected?
b) Dwight, ano
Solutions to practice problems
Problem 1 I should have asked for the probability of getting swept :(
a) p = 95/162 = 0.586.
b) Say all 5 games are played regardless of how many the Red Sox win. Then they win the best-of-5 if
they win 3,4, or 5 of these ga
Probability Practice Problems Solutions
Probability densities integrate to 1. The trick here is to rewrite these in terms of known probability densities.
a) Write it as a normal density with mean = 0 and standard deviation = 1/2.
dx = 2
Discrete distribution solutions
1. There are 2 ways of approaching this problem.
Consider the games they play Bernoulli trials with probability of success p = 0.6. In a best-of-5 series,
Bill wins if he wins 3 games. So if you dene the random va