Probability and Statistics for Biological Sciences and Engineering
550 311

Fall 2014
PROBABILITY AND STATISTICS 550.310 SUMMER I 2012
MIDTERM EXAM
Name:
No document. No calculator. The exam is worth 105 points.
1. Multiple Choices (25 points)
Clearly circle the letter of the most correct answer to each question.
stands for Union or OR, s
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550.311 HW 4 Solutions
1. Suppose X Geom(p) where X counts failures so that P[X = 0] = p. Show that for
any s, t Z with t s 0 that P[X tX s] = P[X t s]. Explain why this
property is called the memoryless property.
Solution:
Proof:
+
P [X t] =
+
P [X =
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550.311 HW 3, Due in Section 2/18
You must (1) Put your name and section number on top of your HW and (2) staple your
HW!
Please turn in:
(1) Suppose that in Hinkley only 200 out of the 3644 people in the Census tract had high
exposure to hexavalent ch
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550.311 HW 2, Due in Section 2/11
By section 2/11 you should have skimmed Ross 1.11.5 2.12.3,2.6 and read carefully all of
Chapter 3.
You must (1) Put your name and section number on top of your HW and (2) staple your
HW!
Please turn in:
(1) A life i
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550. 311 Exam I Practice Problems
1. We randomly put n balls into N boxes. Whats the probability that each box has at
most ball.
2. There are 12 red balls and 3 blue balls. Randomly put these 15 balls into 3 boxes such
that each box has 5 balls. Whats
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550. 311 Exam I Practice Problems
1. We randomly put n balls into N boxes. Whats the probability that each box has at
most one ball.
N !/(N n)!
Solution N (N 1) (N n + 1)/N n =
Nn
2. There are 12 red balls and 3 blue balls. Randomly put these 15 balls
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550.311 HW 3, Due in Section 2/18
You must (1) Put your name and section number on top of your HW and (2) staple your
HW!
Please turn in:
(1) Suppose that in Hinkley only 200 out of the 3644 people in the Census tract had high
exposure to hexavalent ch
Probability and Statistics for Biological Sciences and Engineering
550 311

Spring 2014
EN.550.311 HW 4, Due at the end of class on Friday
3/7
You must (1) Put your name and section number on top of your HW and (2) staple your
HW or it will not be graded!
Please turn in:
(1) Suppose X Geom(p) where X counts failures so that P[X = 0] = p. Sho