Suppose you have a two-period model OLG in discrete time

Suppose you have a two-period model OLG in discrete time. Lt agents are born in time t, where Lt = (1+n)tL0. Normalize L0 = 1 and let n > 0. Preferences of a young agent born in time t are time separable:
u(c1t,c2t+1) = 2(c1t)0.5 + 2(c2t+1)0.5,
where c1t denotes consumption in period t; c2t+1 denotes consumption in period t+1 of an old agent born in t. The initial old agents want to consume as much as possible. Each young agent is endowed with y units of the consumption good. The old have no endowment whatsoever. There is a storage technology that allows to convert one unit of period t goods into 1+r units of period t+1 goods. There is a social security system that is "pay-as-you-go". In each period t the government taxes the young and uses the receipts to make transfers to the old. We consider a per capita tax on the young that is constant over time, i.e. ?t = ? for all t = 0, 1, 2, ...

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Consider a two-periodOLGmodel, where each generation consists of n people. There is no production in this model and each person receives constant income Y. Young persons can buy government bonds when young and sell them when old. Let 1 denote the first period (young) and 2 the second period (old). For simplicity, assume consta

1. Compute the unit-pulse response h[n] for n=0, 1, 2 for the discretetime system
y[n+2] + 1/2y[n+1] + 1/4y[n] = x[n+1] - x[n]
2. Determine if each of the following signals is periodic. If a signal is periodic, what is its period?
x[n] = 3sin(100n)
x[n] = 4cos(1.5πn)
3. For the discrete signals defined as the

1. Suppose that a variable x has the following distribution function:
x p(x)
3 0.23
5 0.41
9 0.36
What is the population mean?
2. Suppose that a variable x has the following distribution function:
x p(x)
1 0.18
6 0.16
9 0.15
24 0.51
What is F(9)?
3. Suppose that a variable x has th

Supposeyou are playing a simple card game with three special cards:
- A blue card that is blue on both sides,
- A red card that is red on both sides, and
- A mixed card that is blue on one side and red on the other.
All the cards are placed into a hat and one is pulled at random and placed on a table. The side facing up i

Give an example representing a discrete probability distribution and another example representing a continuous probability distribution. Explain why your choices are discrete and continuous.
Please provide me an insightful analysis of the question is lengthy in response and include specific examples.

Attached are three problems that I am working. Any assistance would be greatly appreciated.
For a discrete-time signal x[n] with the z-Transform:
X(z) = z
________________________________________8z2-2z-1
find the z-Transform, V(z) for the signal v[n] = e3nx[n].
See attached for the rest of the

Choose a person aged 19 to 25 years at random and ask, "how many times haveyou worked out in the past?" Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get:
Days 0 1 2 3 4 5 6 7
Probability 0.68 0.05 0.07 0.08 0.05 0.04 0.01 0.02