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
3
a) and b), the s
Counting Problems
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
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-
line model
Inter
Probability Practice Problems
Problem 1
Using concepts from this class, compute the following integrals. (tricks like u-substitution, integration by
parts, etc. wont work)
2
e2x dx
a)
x1/2 ex dx
b)
0
Problem 2
Let X and Y be independent Poisson random var
MA581 Practice problems
Problem 1
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
Problem 1
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.
e
2x2
dx = 2
1
Counting Solutions
1. For this, you want to use the BCR. Order counts here since we are dealing with words. Note the
following:
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
Discrete distribution solutions
1. There are 2 ways of approaching this problem.
Method 1:
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
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
MA581 Fall 2015
PROBABILITY
Instructor: Prof. Murad Taqqu, MCS 252, Tel 617-353-3022. Email: murad@math.bu.edu
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
:5: Mr». J, _, (Ann :11: X t "m K _, _ _ w
__,V w m_4~ 3K _ 4 5 . _ M # , , ,
1w 1V V L__ __ _ w
2 ,,,, _, g P
"(0
Iw M7 32 dvawn of: w: , s. *-
~ 3? n. g» A {ll/p _ w".
Q i 0 3 P 931%) {F'PM '33i%3@=% eé
Q" 2) mm): wm a2)
X m) A