E[X]E[1/X] 2 1, if X > 0, E[X] < oo, E[1/X] < 00.O TrueFalse2E[X|Y] = E[X|2Y]%3DTrueO FalseIf (N,}20 is a Poisson process, then (N2- N,l20 is a Poisson process.O TrueFalse

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Answered: E[X]E[l/X] > 1, if X > 0, E[X] < o,…

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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Let (Nt)t>0 be a Poisson process with parameter λ=2, Find the following: (a) E(X3X4)
1 Suppose that X is a stochastic process with dynamics dXt = µdt +σdWt , where W is a P-Brownian motion. The drift µ and the volatility σ are both constants. Find if there is a measure Q such that the drift of process X under Q is η(∈ R) instead of µ.
Prove the following property of the compound Poisson process:1. E(xt) = λ t E(Y).
Let (Nt)t>0 be a Poisson process with parameter λ=2. Find the following: (c) E(S3S4)
B) Let dP/dt =.5P - 50. Find the equilibrium solution for P. Furthermore, determine whether P is intially increasing faster if the initial population is 120 or 200.
A time series with a periodic component can be constructed fromxt = U1 sin(2πω0t) + U2 cos(2πω0t),where U1 and U2 are independent random variables with zero means andE(U21 ) = E(U22 ) = σ2. The constant ω0 determines the period or time ittakes the process to make one complete cycle. Show that this series is weaklystationary with autocovariance functionγ(h) = σ2 cos(2πω0h
Let (Nt)t≥0 be a Poisson process. Explain what is wrong with the following proof that N3 is a constant.E ((N3)2) = E(N3N3) = E(N3(N6-N3)) = E(N3)E(N6-N3) = E(N3)E(N3) = E(N3)2.Thus, Var(N3) = E((N3)2)-E(N3)2=0, which gives that N3, is a constant with probability 1.
Consider a series xt generated by the moving average process as: xt = µ + εt + θ1εt−1, where εt are independently identically distributed random variables with E(εt) = 0, and V ar(εt) = σ2. Calculate the unconditional mean and the unconditional variance of xt. What is meant by saying that a process like xt is invertible? What condition would assure that xt is invertible? If θ = 0.75, does xt satisfy the invertibility condition? What shapes of the ACF and PACF functions do you expect for xt? Derive the first 4 autocorrelations for this process (τ1 up to τ4). Carefully write the equations for the 1, 2, 3 and 4 step ahead forecasts for xt.
If C(x)=∞∑n= (2n+1/2n+2)x^2n and S(x)=∞∑n=0 (2n+2/2n+3)x^2n+1 find the power series of C(x)−S(x)C(x)-S(x).
Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_tdt + σS_dW_t, where µ and σ are constants and r is the risk-free rate. 1. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Xt = S_t^n , where n is a constant. 2. Compute E[X_t] and Var[X_t]. 3. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Y_t = S_tert
At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in state 2 on one observation, then it is 3 as likely to be in the state 2 as state 1 on the next observation. (a) If the particle is in state 1 on the fourth observation, what is the probability that it will be in state 2 on the sixth observation and state 1 on the seventh observation?
A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next custom

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E[X]E[l/X] > 1, if X > 0, E[X] < o, E[1/X] < co. O True O False