Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250(B) Quiz #2
2016.09.26
Student ID:
Name:
1. There are three coins C1 , C2 , C3 in an urn and their probabilities of heads are 1/4, 1/2,
3/4 respectively. One coin is chosen from the urn (uniformly) and that coin is tossed twice.
Given that the two t
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250(B) Quiz #3
2016.10.10
Student ID:
Name:
1. Suppose that X has density function
ax if 0 < x < 1
f (x) =
0
otherwise.
Find the constant a. Also, find limn nE[X n ]
[Solution]
Z
x
a = 2 and thus, F (x) =
2tdt = x2
0
FX n (x) = P (X x1/n ) = x2/n
2 2/n
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250 Ch.04 Solutions
(7, 13, 16, 20, 26, 29, 30, 36, 39, 42, 49, 53, 54, 56, 57)
7. The probability that a given radio tube will last less than 150 hours is
Z 150
100
1
dx = .
2
x
3
50
Therefore, the desired probability is
5 1 2
1
80
( ) (1 )3 =
.
2 3
Korea Advanced Institute of Science and Technology
Introduction to Probability and statistics
MAS 250

Fall 2016
MAS250 Ch.03 Solutions
(6, 7, 13, 14, 22, 30, 33, 41, 48)
6. (a) EF c Gc
(f) E c F c Gc
(b) EF c G
(c) E F G
(g) E c F c E c Gc F c Gc
(i) EF Gc EF c G E c F G
7. (a) S
(b) 0
(d) EF EG F G
(c) E
(e) EF G
(h) (EF G)c
(j) S
(d) EF
(e) F EG
13. (a) Since E =