Let X1,..., X, be an iid random sample from the Binomial(k, p) distribution, where p is known butk is unknown. For example, this could happen in an experiment where we flip a coin that we knowis fair and observe x; heads, but we do not know how many times the coin was flipped. Supposewe observe values x1,..., xn of our random sample. In this problem, you will show that there is aunique maximum likelihood estimator of k.(a)What is the likelihood function, L(k)? Why is maximization by differentiationdifficult here?(b)of k. What is the value of the likelihood when k < ¸max x;? Based on this, what can youWe have to take a different approach to finding the maximum likelihood estimatori=1,...,nconclude about the range of values the maximum likelihood estimator can take?(c)at k and k +1,Based on part (a), what can you conclude about the ratio of two likelihoods evaluatedL(k)L(k – 1)'L(k + 1)L(k)|for k in the range found in part (b)?(d)Using part (c), show that the maximum likelihood estimator is the value of k thatsatisfiesnnII (1 - ) < (1 – p)" < II(!Xik +1i=1i=for k > max;=1,...,n i.(e)part (d). This description of the MLE for k was found by Feldman and Fox (1968).Show that there is only one unique integer value of k that satisfies the equation in

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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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In large corporations, an "intimidator" is an employee who tries to stop communication, sometimes sabotages others, and, above all, likes to listen to him or herself talk. Let x1 be a random variable representing productive hours per week lost by peer employees of an intimidator. x1: 7 3 6 2 2 5 2 A "stressor" is an employee with a hot temper that leads to unproductive tantrums in corporate society. Let x2 be a random variable representing productive hours per week lost by peer employees of a stressor. x2: 3 3 10 8 6 2 5 8 x1: 3.8571 s1: 2.1157 | x2: 5.625 s2: 2.8754 | Level of Significance: 0.05 | H0: ?1 = ?2; H1: ?1 < ?2 got the value of the sample test statistic wrong but its unchangeable. I need help finding the 90% confidence interval for ?1 − ?2 (rounded answer to 2 decimals)
Assume a sample X1，X2 ，，Xn are i.i.d. random variables from a distribution given below.
Ch 7: Homework Question 6 of 6 - / 2 Current Attempt in Progress A population proportion is 0.61. Suppose a random sample of 662 items is sampled randomly from this population. Appendix A Statistical Tables a. What is the probability that the sample proportion is greater than 0.62? b. What is the probability that the sample proportion is between 0.57 and 0.66? c. What is the probability that the sample proportion is greater than 0.59? d. What is the probability that the sample proportion is between 0.59 and 0.60? e. What is the probability that the sample proportion is less than 0.52? (Round values of z to 2 decimal places, e.g. 15.25 and final answers to 4 decimal places, e.g. O.2513.) a. b. C. d. e. 52,196 étv
2. If a discrete random variable X follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20, the value of P(|X - 14| < 5) will be: 1 A. 5 1 В. 4 1 С. D.
Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given in Table P(x) 3 0.05 4 0.40 5 0.30 6 0.15 7 0.10 Table a. In words, define the random variable X. b. What does it mean that the values zero, one, and two are not included for x in the PDF?
There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable Z is the sum of X and Y. That is, Z = X + Y. Calculate the mean of Z.
Suppose x is a uniform random variable with values ranging from 40 to 90. Find the probability that a randomly selected observation exceeds 55.
9. Carboxy- hemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood (Reference: A Manual of Laboratory and Diagnostic Tests by F. Fischbach). Let x be a random variable rep- resenting percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n-12 blood tests given to a heavy smoker gave the following results (percentage of carboxyhemoglobin in the blood): 9.1 9.5 10.2 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 Where = 10.49 and s = 1.36. A long-term population mean u -10% is considered a health risk. However, a long- term population mean above 10% is considered a clinical alert that the person may be asymptomatic. We will investigate the claim: the data indicate that the population mean percentage is higher than 10% for this patient? Use a = 0.05. a. Find the test statistic. b. Find the critical…
1. For each random variable described below, give its distribution (which will be Binomial, Geometric, Hypergeometric, Pascal, or Poisson) and the parameters of that distribution. (a) You are working on a difficult homework assignment with 5 problems. Every minute, you have an idea for the problem you are working on, but it only has a 5% chance of working. If it doesn’t work, you keep working on that problem, and if it works, you move on to the next problem. The random variable W is the time (in minutes) that it takes you to finish the homework assignment. (b) A standard 52-card deck is split equally between two players. The random variable X is the number of aces received by the first player. (There are four aces in the deck.) Note: this is a key parameter when playing the “card game” “War”. (c) Every time you turn on the light, the light bulb has a 1% chance of burning out and you have to replace it. The random variable Y is the number of times you turn on the light before you have…
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of “girls” (g) and “boys” (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbb, then R(bbb)=0. Suppose that the random variable X is defined in terms of R as follows: X=R^2-2R-1. The values of X are given in the table below.
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbg, then R(bbg) = 1. Suppose that the random variable X is defined in terms of R as follows: X=R- - 2R-4. The values of X are given in the table below. Outcome bbb ggb bbg gbg gbb bgg bgb gg Value of X-4 -4 -5 -4 -5 -4 -5 -1 Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X Px (x) E 1:48 PM 3/21/2022 hp Compag LAI956X 立

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