It is known that a sample consisting of the values 2, 3, 4, 3, and 4 comes from a discrete randomvariable with the probability mass functionPx(x) = p(1 - p)x-1Find the maximum likelihood estimate (MLE) of p

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Answered: It is known that a sample consisting of…

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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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…
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x = 1,2,...,9. (This 2. Let X be a discrete random variable with pmf f(x) = log₁0 distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading significant digit in numbers occurring in many datasets.) a) Verify that f(x) satisfies the conditions of a pmf. b) Find the cdf of X.

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It is known that a sample consisting of the values 2, 3, 4, 3, and 4 comes from a discrete random variable with the probability mass function Px(x) = p(1 - p)x-1 Find the maximum likelihood estimate (MLE) of p