Assume we want to estimate the parameters of a Bernoulli distribution p(x; 0) = 0² (1 - 0)¹-² using maximumlikelihood estimation with the Bayesian approach. We are given univariate binary data [₁, 2,...,n] and theprior distribution has the form of p(0) = 0.40310 (1-0). Find the estimated parameter 0.Show all of your calculations.

Answered: Image /qna-images/answer/74c5ba50-2441-4968-9749-b2bae9357474.jpg

Answered: Assume we want to estimate the…

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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The probability that the Air Conditioning of a brand new car is defective is 10%. Let X be the number of cars with defective AC in a sample of size 100. (a). Find P(X < 6) exactly. (b). ) Find P(X < 6) approximately, using a Poisson approximation (c). Find P(X < 6) approximately, using a normal approximation. Note: For parts (a) and (b), you only need to provide a formal expression each. For part (c), you need to compute the numerical values using the Q-function table (Table 4.2) from the textbook.
Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
Let X1, ..., Xn be a sample from an exponential population with parameter λ.(a) Find the maximum likelihood estimator for λ. (b) Is the estimator unbiased?(c) Is the estimator consistent?
If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean and variance of X? Round to three decimal places
Let X1, . . . , Xn be iid with pdf f(x) = 1 x √ 2πθ2 e − (log(x)−θ1) 2 2θ2 , −∞ < x < ∞, and unknown parameters θ1 and θ2. Find the maximum likelihood estimators for θ1 and θ2, respectively
the pdf of a random variable x is given by f(x;θ) = θx^θ−1 x ∈ (0,1). find the maximum likelihood estimate of θ
Suppose X1,...,Xn are iid with PDF f(x | θ) = 2x/θ2, 0 < x < θ. (a) Write out the joint PDF f(x | θ), and write the likelihood function L(θ | x). (b) Find the MLE for θ. (c) Find the MLE for the median of the distribution.
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
If X is a uniformly distributed random varibale with a=9 and b=16, then Calculate the variance of X? Round to three decimal places
Suppose that X is a random variable with the density:f(x) = ( θxθ−1 if x ∈ (0, 1) 0 if otherwise The parameter θ > 0 is to be estimated. Suppose that x1 = 0.3, x2 = 0.6 are the sample data. Get the estimate of θ(a) using the Moment Method;(b) using the Maximum Likelihood Method.
Consider a random sample X_1, X_2, ... , X_n from the pdf f(x; θ) = (θ+ 1)x^θ 0≤x≤1 where θ > −1 Use the Maximum Likelihood Method to obtain an estimator of θ and then compute the estimatefor the following random sample of four observations: 0.42, 0.37, 0.64, and 0.55.
A simple random sample of size n =66, is obtained from a population that is skewed left with =33 and =3. . Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?(A) Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (B) Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. (C)No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x, become approximately normal as the sample size, n, increases. (D) No. The central limit theorem…

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