Solution to HW #5 36-220/247
1. (7.2, 10 pts) Y1 , . . . , Yn are Poisson()
(a) To nd the unbiased estimators, need to nd their expected value and check if it is equal
to what they are estimating, .
1
E(1 ) = E(Y ) = n E(
n
i=1
Yi ) =
1
n
n
i=1
E(Yi ) =
1
Solution to HW #2 36-220/247/747
1. (3.33, 20 pts) (a) Dene the following events:
A = cfw_ Alarm A goes o , B = cfw_ Alarm B goes o , I = cfw_ There is an intruder .
P (A|I) = 0.9
P (B|I) = 0.95
P (A|I C ) = 0.2
P (B|I C ) = 0.1
(b) Both systems sounding
Part I: For each the following, simply give the answer. It is not required that any derivation
0r justication be provided, and there is no partial credit. Each of these is worth three points.
1. Suppose that events A, B are independent events. What can b
Solution to HW #6 36-220/247
1. (8.10) (2 points)
Let stand for the egg-hatching rate.
H0 : = 0.5
Ha : > 0.5
2. (8.16) (2 points each part)
(a): Let = mean surface roughness.
H0 : = 2
Ha : = 2
(b): Since n = 20, we must use the small-sample test (t-test,
Solution to HW #4 36-220/247/747
1. (5.30, 15 pts)
Let Y be the injected quantity, so Y is normal with mean = 10, sd = 0.2.
(a) Want P(underlled) = P (Y < 10)
= P ( Y 10 < 1010 ) = P (Z < 0) = 1
.2
.2
2
(b) Prot = $230 - reprocess cost - ll cost
= 230 10
Solution to HW #9 36-220/247/747
1. (11.23)
(a.) (2pts) The regression output is as follows:
Regression Analysis: Voltage versus Disperse Phase Volume, Salinity, .
The regression equation is
Voltage = 0.998 - 0.0224 Disperse Phase Volume + 0.156 Salinity
Solution to HW #7 36-220/247/747
1. Let X denote the sample mean. (5 points each part)
(a): P(Type II error) = P(fail to reject | = 10.5)
= 0.05 corresponds to a z-value of 1.65. So the rejection region is X > 10 + 1.65(0.5/ n).
When n = 25, the rejectio
Solution to HW #3 36-220/247
1. (4.5, 10 pts) (a) Y = Number of free links.
There are two total links, so the possible values of Y are 0, 1, 2.
(b) We must nd P (Y = 0), P (Y = 1), P (Y = 2). (Actually, nding two of the three is
enough)
Dene events A = cf
Solution to HW #1 36-220/247
1. (a) The population of interest in this case is the thion level in air as a result of contamination
due to extensive application of pesticides to crops, at any location and at any date. (Alternatively, the population could r
36-220/247/747 Exam Three April 11, 2014
VERSION A
Name
Email
Group
Part Possible Points
I
16
II - 1
8
II - 2
5
II - 3
5
Free
1
1
Score
36-220/247 Exam Three April 16, 2014
VERSION B
Name
Email
Group
Instructions:
1. You have 50 minutes to work on the exa