Solutions
Note: Version 2.0 completed 12/23/04. Includes solutions to nearly all problems. Thanks to Ted Jiang for generating many of the SPICE simulations.
Chapter 1
1.1 Starting with 42,000,000 transistors in 2000 and doubling every 26 months for 10 yea
Homework Set #1 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and ll in the gaps.
1.1 a) S1 = cfw_H, T , S2 = cfw_1, 2, 3, 4, 5, 6 and S3 = cfw_0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
b) The o
1. (10 marks) Random variable X has the following cdf:
a. Derive AND plot the pdf of X.
b. Find
c. Find .
a)
f x ( x) =
d
FX ( x )
dx
x<0
0
3
e 2 x
0 x <1
2
= 1
4 ( x 1) x = 1
3 e 2 x
x >1
2
b)
1
1
P[ < X < 2] = FX (2 ) FX ( )
2
2
3 4 3 3 1
Homework Sets #5 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and ll in the gaps.
3.36. (a)
pX (x|X < 4) =
P [cfw_X = x cfw_X < 4]
P [cfw_X = x cfw_X < 4]
=
P [X < 4]
p1 + p2 + p3
T
Homework Set #2 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and
ll in the gaps.
2.23 P [cfw_c] = P [cfw_c, d] P [cfw_d] = 2/8, P [cfw_b] = P [cfw_b, c] P [cfw_c] = 4/8, P [cfw_d] =
ECE 302, Oct12,2011
Q1. An urn contains ten identical balls numbered 1 to 10. Suppose you pick two
balls from the urn in succession without replacement. Find the probability of the
following events:
a. The two balls are even numbered.
b. One of the two ba
Homework Set #6 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and
ll in the gaps.
4.17 (a)
1
1
c(1 x2 )dx = 1; therefore, c = 3/4.
(b)
FX (x) =
r2
4.
1
8
4
k = 3
1
x3
3)
+
x 1
1 x 1
Homework Set #7 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and ll in the gaps.
1
4.62. a) P [X x] = 1 ex = r/100 (r) = x = ln(1
2.3/ (95) = 3/ (99) = 4.6
(90) =
b) P [X x] = 1
Homework Set #4 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and
ll in the gaps.
2.82 To examine whether the events A, B and C are independent, we should verify independency rule. T
Homework Set #3 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and ll in the gaps.
2.43 There are 24 choices for special character, 10 choices for a number, and 48 choices for a lette
UNIVERSITY OF TORONTO
Edward S. Rogers Sr. Department of Electrical and Computer Engineering
ECE302H1F Probability and Applications
GENERAL COURSE INFORMATION Fall 2013
INSTRUCTORS
Prof. Frank Kschischang is in charge of Lecture Section 1. Contact informa
Homework Set #8 Solutions
Note: These solutions are intentionally abbreviated; you should attempt to work out the problems on your own and ll in the gaps.
4.102. X ( ) =
E [X ] =
fX (x)ejx dx =
1 dX ( )
j
d | =0
=
E [X 2 ] =
1 d X ( )
j2
d 2 | =0
1
ejx dx