iidX1,..., XnGeo(p) where 0 0; B>0]a conjugate family forsamples from the Geometric distributions [Geo(p): 0 0 are known constants.C-Derive the Bayes estimator of p.d- Express the estimator in part (c) as a weighted average of the prior mean of p and theMLE of p.

Answered: Image /qna-images/answer/d17f608f-6b98-4278-a9df-e312125e3581.jpg

Answered: а- Find the maximum likelihood…

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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Suppose we are interested in investigating the lifespan of a Texas Instrument calculator and we model the lifespan using an exponential distribution with unknown parameter (A). If we test 5 calculators, and their lifetimes are 2, 3, 1, 3, and 4 years, respectively, (a) What is the maximum likelihood estimator for λ? (b) What does it mean in words?
The relatively efficient estimator has the variance. ...... .............. O a. maximum O b. least O c highest O d. atmost O e. None of these.
19. Find the maximum likelihood estimator for the parameter h of Poisson distribution.
A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
Q2: Let x1,X2, . , Xn and y1, y2, ..., Ym represent two independent random samples from the respective normal distributions N(H1,07) and N (H2, 03). It is given that of = 30, but ožis unknown. Then 1. A random variable that can be used to find a 95% confidence interval for - is (x- y) - (H1 - H2) А. ns3 + ms n+m. 3(n+m-2)"tm, nm O A (x – y) – (41 – H2) В. ns? + ms; n + m. (n + m – - 2) пт (x – y) – (41 - H2) С. ns3 + mS;_n+3 3(n+ m-2) ("+3m nm Ос
If there is an association between two variables, which is true? 1- the scores of the cases are approximately equal 2- the distributions of the scores approach normality 3- all of the scores are in the same row in the bivariate table 4- the conditional distributions of Y change
The lifetime of an electronical component is to be determined; it is assumed that it is an ex- ponentially distributed random variable. Randomly, users are asked for feedback for when the component had to be replaced; below you can find a sample of 5 such answers (in months): 19,23,21,22,24. Fill in the blanks below. (a) Using the method of maximum likelyhood, the parameter of this distribution is estimated to 2 = WRITE YOUR ANSWER WITH THREE DECIMAL PLACES in the form N.xxx. DO NOT ROUND. (b) Let L be the estimator for the parameter of this distribution obtained by the method of moments (above), and let H be the estimator for the parameter of this distribution obtained by the method of maximum likelyhood. What comparison relation do we have between L and M in this situation? Use one of the symbols to fill in the blank. L M
Q.6 (a) Write the gamma distribution for a random variable X denoted by X~F(a, B); its mean, variance and moment generating function (No derivation is required). (b) What is the relationship between gamma distribution and chi-square distribution?
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The two assets, X and Y, whose returns are shown in the multivariate distribution to the right, have the following expected returns, variances, covariance, and correlation: mX = 13.00%; mY = 12.50%; sX = 3.317%; sY = 2.500%; Cov(X,Y) = -.0004; rXY = -.45 a) What is the expected return and standard deviation of a portfolio that is 50% Asset X and 50% Asset Y? b) What is the expected return and standard deviation of a portfolio that is 75% Asset X and 25% Asset Y? c) Which of the preceding portfolios ((a) or (b)) is better? Why? show all work and formulas used in excel

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