25): Suppose that, for 0, B E R, we findVnB - Bse the Delta method to find the asymptotic distribution of the following:1. 032. cô+â3. 0/B, if 3 +04. 03 + 0B2

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Answered: 25): Suppose that, for 0,3 E R, we find…

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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2. A random variable X has the exponent ial distribution as f(x) = Xe¯, x>0 %3D a) Find the mom ent generating function, Mx(t). b) Use the moment generating funct ion to find the mean and variance of X.
(a) Given that X is normally distributed with mean 10 and ?(? > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given: Φ(1) = 0.8413 and Φ(−1/2)=0.3085, where Φ(?) = ?(−∞ < ? < ?)such that ?~?(0,1). (b) Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter ? = 2, time being measured in minutes. What is the probability that a shower will last more than three minutes? If a shower has already lasted for 2 minutes, what is the probability that it will last for at least one more minute?
3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.
If X and Y are two independent uniform distribution with X(0 ,4) and Y(0,6). Find the joint pdf f (x.y). Find P(2.5<X<3.5,1<Y<4)
3A) Given P=822-30Q2 and MC=12+9Q find the consumer surplus (CS) (Hint: TR to MR and optimum quantity is MR=MC). B) S=200000 e5find the growth rate of S. C) MC=24eQ and FC=72 Find the total cost. D) The probability of waiting in bus station is given with the frequency distribution f(t)= 1/16 t3 find the probability that your waiting time will be between 1 and 2 minutes?
Let X1, . . . , Xn ∼ iid Unif(0, θ). (a) Derive an asymptotic distribution for the MOM estimator ˜θ = 2X¯ of the form.(b) From this choose an approximate pivot and interval to get an interval that asymptotically has100(1 − α)% coverage.
Assume that X1, X2, X3 ∼ Exp (λ) are independent and evenly distributed with the distribution Exp (λ = 1). (a) Determine the distribution of Y = X1 + X2 + X3 and state its PDF f (y). (b) Determine the distribution of U = 2Y
State the CLT for independent identically distributed real RVs with mean u and variance a². Suppose that X. X,. . . are independent identically distributed random variables each uniformly distributed over the interval [0, 1]. Calculate the mean and variance of In X. Suppose that 0
Let 0 be the maximum likelihood estimator of the parameter 0. We are given that lim, 00 E(0) = 0 and 1. Then what is the asymptotic distribution of 0? %3D CRLB(@) Var(0) lim 00 O a. @~N(0,CRLB(0)). O b. ê- N(0, CRLB@) Oc O~ N(0,CRLB(0)). O d. - N(ô. CRLB(@).
Use Itô Isometry To Calculate The Variance Of Each Of The Following
1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.
page 328 5.2.2

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25): Suppose that, for 0,3 E R, we find võ (:) -(C) ( ) Vn В — В O B0 BB e the Delta method to find the asymptotic distribution of the following: 1. 0B 2. eô+â 3. ô/3, if 3 + 0 4. 03 + 032