Question 3Suppose that the true (unobserved) log price p of an asset follows the model:Pt = Pt-1 + at, where {at} is sequence of iid N(0, 1) random variables. Suppose that theobserved log price p, follows the model: p = Pt+et, where {e} is another sequence ofiid N(0, 0.25) random variables and {e} and {a} are independent. Let r=pr-pr-1 be theobserved log return. Calculate the lag-1 and lag-2 autocorrelations of r₁.

Given that the true (unobserved) log price of an asset follows the model:, where is sequence of iid…

Answered: Suppose that the true (unobserved) log…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Example 9-53. (a) Find the p.d.f. of Xr) in a random sample of size n from the exponential distribution: f(x) = a e i, a>0, x 20. (b) Show that X) and W, = X9-X¢», r < s, are independently distributed. %3D
(a) Determine the value of k for a valid pdf.(b) Complete the cdf of X .(c) What is the expected total deduction on a randomly chosen form?(d) Let Y = ln(X /5), where ln(·) is natural logarithm. Determine the pdf as wellas the cdf of Y , and further identify which common distribution that Y follows?
A medical researcher says that less than 82% of adults in a certain country think that healthy children should be required to be vaccinated. In a randon sample of 300 adults in that country, 78% think that healthy children should be required to be vaccinated. At a = 0.10, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and Ha Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) CA. Less than 82 % of adults in the country think that healthy children should be required to be vaccinated. O B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not %. O C. More than % of adults in the country think that healthy children should be required to be vaccinated. O D. % of adults in the country think that healthy children should be required…
3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
Suppose model (XY, XZ, YZ) holds in a 2 x 2 x 2 table, and the common XY conditional log odds ratio at the two levels of Z is positive If the XY and YZ conditional log odds ratios are both positive or both negative, show that the XY marginal odds ratio is larger than the XY conditional odds ratio.
X = factorial(3) def factorial(n): if n == 1:return 1else:return n* factorial (n-1) def factorial(n):if n== 1: return 1else: 2return n * factorial(n-1) def factorial(n):if n==1: return 1 else:return n* factorial (n-1) Provide a relationship with the domain subset of the integers that is proven using mathematical induction
Consider an economy where each worker is employed in either agriculture or services. Assume that log earnings of a worker are wo = 4o + €o if she is employed in agriculture and wi = µ1+€1 if she is employed in services, where µo and H1 are constants, ɛo ~ N(0, o3), and e1 - N(0, o?). Assume also that the correlation between earnings in the two sectors is p = g01 where oo1 = Cov(Eo, E1). Workers can be employed in agriculture at no cost, but they incur a cost C = T exp(wo) if they choose to work in services. Finally, assume that workers maximize their net earnings. Each worker knows all the parameters relevant to her decision. (a) Derive a linear approximation of the equation that determines whether an individual chooses services or agriculture. Assume that C is small compared to exp(wo), so you can ignore the error involved in this approximation. (b) Define v = €1 chosen worker is employed in services as a function of z, where z = (Ho – H1 +7)/0,. (c) How does this probability change…
Assume a 3-year select period and the following: Ultimate Rates Effects of Selection Age x 25 0.00185 9x] = qx * .7 26 0.00205 9[x]+1 = qx+1 .8 27 0.00225 9[x]+2 = qx+2 * 9 28 0.00245 29 0.00265 Complete this table of life counts: [x] Ix+3 x+3 1000 25 26 27 25 28 26 29 27 30
The functions i)= e **2f,(x) = e*-3 %3D are O A. Insufficient information to conclude None of them O B. O C. Neither linearly dependent or independent OD. Linearly independent O E. Linearly dependent
Let i, denote the effective annual return achieved on an equity fund achieved between time (t-1) and time t. Annual log-returns on the fund, denoted by In(1+i), are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and σ = 14%. An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%.
2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).
In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.

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