Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 <0 <1). Let X₁, X2, X, be a random sample of size n from the population of X.(e) Show how the mle ofis related to its mme. Explain if it is always true.(f) Verify ifX, is a sufficient statistic for or not.(g) Justify if = is an unbiased estimator for 0.X

Suppose the random variable follows a geometric distribution with parameter .Then the pmf of…

Answered: Suppose the random variable, X, follows…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 43 and standard deviation ? = 9. Find the following probabilities. (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60
If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?
The random variable, x is a water quality parameter, suspended solids with units of parts per million (ppm). A sample size of 60 yields a mean of 59.87 ppm, and a standard deviation of 12.5 ppm. Water quality criteria requires that the suspended solids do not exceed a mean, µ, = 50 ppm . Test the hypotheses H.: u = µ, vs. HA: u > H. (right-tailed test) at a level of significance of 5 % and assume the pop variance is known.
Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.
Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?
Suppose that average rainfall in your city is normally distributed, and for the past 36 months, the rainfall has been 0.5 inches per day on average with a standard deviation of 0.16. Let x be a random variable that has a normal distribution and represents the rainfall in inches per day. Using a 0.05 level of significance, you want to test the hypothesis that monthly rainfall has been 0.7 inches per day on average. What conclusion do you make from your test? Select one: a. Reject H0; the average rainfall is not 0.5 inches. b. Reject H0; the average rainfall is not 0.7 inches. c. Do not reject H0; the average rainfall is still 0.5 inches. d. Do not reject H0; the average rainfall is still 0.7 inches.
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
level of blood glucose and diabetes are closoly related. Let x bo a random variable measured in milligrams of glucose per deciliter of od. After a 12-hour fast, th random variable x will have a distribution that is approximately normal with mean - 85 and standard deviation 5. What is the probability that for an adult after a 12-hour fast. s less than 7o, b. x is greater than 120?

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