Negative binomial probability function:
is the mean
is the dispersion parameter
Let there be two groups with numbers and means of
1) Write down the log-likelihood for the full model
2) Calculate the likelihood equations and find the general form of the MLE for and
3) Write down the likelihood function in the reduced model (ie. assuming ) and derive the MLE for in general terms
4) Using the above answers only, give the MLE and standard error for where
5) Compute the expected information and the asymptotic variance-covariance matrix of the MLEs in the full model
6) Give the formula for an approximate Wald test of
Negative binomial probability function: is the mean is the dispersion parameter Let there be two groups...
A Pareto distribution is often used in economics to explain a distribution of wealth. Let a random variable X have a Pareto distribution with parameter θ so that its probability distribution function is for and 0 otherwise. The parameters and are known and fixed; is a constant to be determined. a) Assuming that find the expected value and variance of ? b) Show that for 3 ≥ θ > 2 the Pareto distribution has a finite mean but infinite variance,...
Let X1, X2, ..., Xn be a random sample from X which has pdf depending on a parameter and (i) (ii) where < x < . In both these two cases a) write down the log-likelihood function and find a 1-dimensional sufficient statistic for b) find the score function and the maximum likelihood estimator of c) find the observed information and evaluate the Fisher information at = 1. f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...
Let be a simple random sample of a random variable X with density function , . Given the statistic : Calculate a statistic ( function of ) such that its espected value is equal to . Thank you for your explanations We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageに! We were unable to transcribe this imageWe were unable to transcribe this image
(6) The sequence of random variable are independent of each other and they follow the normal distribution . However, the actual value of were not observed, instead we only observed if each is either greater than or equal to 0, or less than 0. And you can use the fact that there is the inverse function that is continuous. Answer the following questions. Find the maximum likelihood estimator of . When , show , where represents conversion of probability....
Let be the distribution function defined by Let be the Lebesgue-Stieltjes measure asociated to . Determine the measurements of the fpllowing sets: We were unable to transcribe this imageF(x) = 0 if 1+r if 2+x? if 19 if I <-1 -1 <r <0 0<r<2 > 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image(-1, 0]υ (1,2) 10, ) U (1, 2 (1 :...
Write A function Markov that take ?, ? and ? as inputs and return the upper bounds for ?(?≥?⋅??) given by the below Markov inequalities as output. For the binomial distribution with mean and variance , we would like to upper bound the probability for . Example: Markov(100.,0.2,1.5) Output: 0.6666666666666666 Which of the following is the correct output for Markov(200.,0.3,1.1)? A. 0.909 B 0.558 C. 0.986 D. 0872 p.n We were unable to transcribe this imageWe were unable to transcribe...
PART C Problem 3. Let Xi.X^...be i.d. sample from a Rayleigh distribution, with parameter > 0: x2 262x> 0 02 We separately computed the ECX2) and found that Ex 28 (a) Find the likelihood function simplifying it as much as possible. Likelihood- We were unable to transcribe this image
Let X be a banach space such that X= C([a,b]) where - ab+ with the sup norm. Let x and f X. Show that the non linear integral equation u(x) = (sin u(y) dy + f(x) ) has a solution u X. (the integral is from a to b). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let X1, X2, ..., Xn be a random sample of size n from the distribution with probability density function To answer this question, enter you answer as a formula. In addition to the usual guidelines, two more instructions for this problem only : write as single variable p and as m. and these can be used as inputs of functions as usual variables e.g log(p), m^2, exp(m) etc. Remember p represents the product of s only, but will not work...
I have found answers to part a and b and just really need help with part c! and the extra if you have time. A= for part a then for part b, I have 5. Wave mechanics: (10 points) Suppose to have the following wave function (-oo 〈 x 〈 +00) r2 a for constants A and a a) Determine A, by normalize V(x). b) Use Ψ(x) to find the expectation values (a), (z2)), and σ,-V(z2,-(z c) Find the momentum...