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5 MATH1055W1
15. [2 marks] Let
A
be a
n × n
matrix that describes a set of
n
inhomogeneous
equations in
n
unknowns:
A ~x =
~
b
. This system of equations has a unique solution
if and only if:
16. [2 marks] The solution of the matrix equation
1 1
2 1
x
y
=
1
1
is
17. [2 marks] If we write
z = 1 + j
in the exponential form, one finds that the two roots
of
z
1 / 2
are
18. [2 marks] A discrete random variable can take the values
x = { 0 , 1 , 2 }
with
probabilities
p =
1
4
,
1
2
,
1
4
. Then, the mean value
μ
and variance
σ
2
are given by
(a)
μ = 1
,
σ
2
= 1 / 2
; (b)
μ = 0 . 6
,
σ
2
= 1
;
(c)
μ = 0 . 2
,
σ
2
= 1 / 3
; (d)
μ = 2
,
σ
2
= 2
;
(e) none of the above.
19. [2 marks] If
X
is a normally distributed random variable with mean
0
and standard
deviation
1
then the probability
P ( X > 1)
equals, to
4
decimal places,
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6 MATH1055W1
20. [2 marks] Consider a function
f ( t, x )
of two independent variables
t
and
x
. If we
introduce the substitutions
u = x + t
and
v = x - t
then
∂f
∂x
is equal to
(a)
-
∂f
∂u
+
∂f
∂v
, (b)
-
1
2
∂f
∂u
+
1
2
∂f
∂v
, (c)
-
1
2
∂f
∂u
-
1
2
∂f
∂v
, (d)
∂f
∂u
+
∂f
∂v
,
(e) none of the above.