Determine whether each system is LTI, causal and/or stable and
with or without memory. Justify answers.
a) y[n + 1] + 4y[n] = 3x[n + 1] - x[n]
b) y[n] = nx[2n]
the following are impulse responses/outputs of
discrete -time LTI systems. Determine whether each system is causal
and/or stable. justify your answers
1. h [n] = 1/5^n u [n]
2. h [n] = 5^n u [3-n]
3. y [n] = 3x [n] - 0.15y [n-1]
4. y [n] = 2e^-x [n]
5. y [n] = n^2 4x [n]
B. Show if the systems defined in 1 to 5 above have
bounded input and output (BIBO) from the summation of their impulse...
A system description that reveals whether a system is stable or
not stable without consideration of other system attributes.
A. Stable system
B. Absolute Stability
C. Marginally stable
D. Optimum control system
Determine whether each of the following statements is TRUE or
FALSE. Justify all the answers in few sentences.
1. In the Ricardian model with 2 goods (Wine and Cheese) and 2
countries (Home and Foreign) and (except otherwise noted) identical
preferences between countries:
(a) If both countries have the same number of workers and Home
has absolute advantages in both goods then Home must have a higher
wage.
(b) The Home country is never made worse off by productivity
growth...
Determine whether each of the following statements is TRUE or
FALSE. Justify all the answers in few sentences.
1. In the Ricardian model with 2 goods (Wine and Cheese) and 2
countries (Home and Foreign) and (except otherwise noted) identical
preferences between countries:
(a) If both countries have the same number of workers and Home
has absolute advantages in both goods then Home must have a higher
wage.
(b) The Home country is never made worse off by productivity
growth...
Determine whether the polynomial is reducible or irreducible in
the given polynomial ring. Justify your answers.
(c) x^4 + 1 in Z5[x]
(e) 2x^3 − 5x^2 + 6x − 2 in Z[x]
(f) x^4 + 4x^3 + 6x^2 + 2x + 1 in Z[x]. Hint: Substitute x − 1
for x.
For each of the following assertions, say whether it is true or
false. Justify your answers.
a) Imagine the next Mars rover stops working upon arrival on
Mars. From this we can deduce that Mars rover is not a rational
agent. (Note that a rational agent is not necessarily perfect, it's
only expected to maximize goal achievement, given the available
information.)
b) Every optimal search strategy is necessarily complete.
c) Breadth-first search is optimal if the step cost is
positive
For each of the following statements, determine whether it is
true or false and justify your answer. a. Every function f : [0, 1]
~ lR has a maximum. b. Every continuous function f :[a, b] ~ lR has
a minimum. c. Every continuous function f : (0, 1) ~ lR has a
maximum. d. Every continuous function f : (0, 1) ~ lR has a bounded
image. e. If the image of the continuous function f: (0, 1) ~...
For each of the following statements, determine whether it is
true or false and justify your answer.
a. If the function f + g: IR --> IR is continuous, then the
functions f :IR --> IR and g :IR --> IR also are
continuous.
b. If the function f^2 : IR --> R is continuous, then so is the
function f :R --> IR.
c. If the functions f + g: IR and g: IR --> IR are continuous,
then...