STA 4032 Midterm Formula Sheet
Chapter 2. Probability
Some Basic Probability Formulas:
(1) P (A B ) = P (A) + P (B ) P (A B ).
(2) P (A ) = 1 P (A) ( A is the complement of A).
P (A|B ) =
P (A B )
, P (B ) > 0.
P (B )
Florida Atlantic University
Instructor: Hongwei Long
STA4032 Midterm Exam
July 11, 2012
No books, notes or other aids, except calculators and the provided formula
sheet, are allowed.
1. A batch contains 36 bacteria cells. Assume that 12 of the cells are n
Solutions to Quiz # 1 (STA 4032)
1. 1. A bin of 40 parts contains ve parts that are defective. A sample of 3 parts is
selected randomly, without replacement.
(a) What is the probability that all three parts in the sample are defective?
(b) What is the pro
Solutions to Quiz # 2 (STA 4032)
1. In an automated lling operation, the probability of an incorrect ll when the
process is operated at a low speed is 0.001. When the process is operated at a high
speed, the probability of the incorrect ll is 0.01. Assume
Solutions to Quiz # 3 (STA 4032)
1. Suppose that the current measuements in a strip of wire are assumed to follow a
normal distribution with mean of 12 milliamperes and a variance of 9 (milliamperes)2 .
(a) What is the probability that a measurement will
Solutions to Quiz # 4 (STA 4032)
1. Let X and Y have a joint probability density function
if 0 x y 2,
fXY (x, y ) =
(a) Find the marginal pdfs of X and Y .
(b) Are X and Y independent? Explain your answer.
(c) Find fY |x (y ) and E (Y |
STA 4032 : MIDTERM PRACTICE EXAM
1. The alignment between the magnetic tape and head in a magnetic tape storage sys-
tem af fects the performance of the system. Suppose that 10% of the read operations are
degraded by skewed alignments, 5% of the rea
2 STAT4032: MIDTERM PRACTICE EXAM
Hint: Determine the value of co rst. T," "
Solution: fLCOdxwz 1 implies co X =1. So co = g 3 km 6M
#2 E(X)= 158 3.1320533: iv fit 114% _cp r
a2 - )Var(X L1 992 - 393261.13 ~ 112 = 535. 3/5 ,
4. Select 15 pieces of parts f
STAT4032: MIDTERM PRACTICE EXAM 3
(b) Let T be the waiting time for next customer. Then T has Exponential distribution
Exp(6). Average waiting time is E (T) = i = % hr. .10 "my
yiivllzl ll 3 l lj Pllel(l'e la -11 as .13 .13
[2(3 41M\P(T_4 +) p(-r43),