2. (This is a fill-in-the-blank question.)Consider the statistical model {P}ee defined as follows:⚫ The parameter space (0,∞) the collection of all positive real numbers.• Each Po presents a continuous distribution characterized by the following probabilitydensity function (PDF)0Pe(x) =5)=(1+x)1+0· 1(x > 0),where 1(x > 0) is an indicator function.Suppose data X1, X2,..., Xn id Po*, where 0* is the unknown true parameter. Please answerthe following questions:The maximum likelihood estimator (MLE) of 0* is ⑦MLE =(a) (0.5(b) (0The Fisher information of the model is I(0)

To solve the given problem involving the statistical model Pθ for (θ∈(0,∞)) with the…

Answered: 2. (This is a fill-in-the-blank…

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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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.
There are two Gaussian curves below (Plots A and B), along with the respective R source codes.Looking at the plots and the source codes provided, identify the parameters of respective Gaussian pdf's (probability density functions) and the numeric value of x in the PDF F(x)express the areas under the curves in terms of F(x). ( Do not calculate those areas.Your answers must be like F(x) or 1- F(x) for a relevant value of x.) Below is the source code and image for part B
Let X denote the vibratory stress (psi) on a wind tur- bine blade at a particular wind speed in a wind tunnel. The article "Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy Engr., 1982: 107-111) proposes the Rayleigh distribution, with pdf e-x²/(20) x> 0 f(x; 0) = { 0² 0. otherwise as a model for the X distribution. a. Verify that f(x; 0) is a legitimate pdf. b. Suppose 0 = 100 (a value suggested by a graph in the article). What is the probability that X is at most 200? Less than 200? At least 200? с. What is the probability that X is between 100 and 200 (again assuming 0 = 100)? d. Give an expression for P(X< x).
2. Let dt Find the average %3D value of f on the interval [o, 1
Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., Xn fxp(x | p) = (1 – p)*-'p for 0 < p < 1 defined on x E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fp|X, (p | Xn).
Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).
a) Suppose that X is a random variable having the following probability density function given by (2(0-x) 02 f(x) = -, x > 0 (0, elsewhere Find the value of c such that an interval from x to cx is a (1- a)100% confidence interval for the parameter 0.
Please give answers of my questions that I have uploaded as an image.
1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
The random variable X has expected value E(X)=4 and Var(X)=4. Here, we want to approximate the probability that X lies in the interval [3.4,5.4] using a transformation to a standard normal distribution Z. Then we will need to calculate the probability that Z lies in the interval [z1,z2] where z1= z2= Suggest z1 and z2 Do NOT attempt to make any sort of continuity correction.
c) Consider the following table: i 1 2 3 4 5 6 7 8 9 10 R₁ 0.7329 0.9755 0.6761 0.0917 0.1584 0.2858 0.8564 0.3628 0.4337 0.5822 Assuming an M/M/1 setup, a service rate of 18 customers every 5 minutes, and a traffic intensity of 0.95 for a pdf characterized by the exponential distribution, compute the correpsonding variates.

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