Let X₁, X₁ be a random sample from a distribution with the following density function.f(x; 0) =0x9-150.00.(4) Find MLE of 9 and its asymptotic distribution.(5) Suppose we obtain a sample of 50 observations from the underlying distribution andfind that log x₁ = 52.5. Construct an approximate 95% confidence interval of 0based on the asymptotic distribution of MLE (20.025 = 1.96, 20.05 = 1.645,20.1 = 1.28)

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Answered: Let X₁, X, be a random sample from a…

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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People with high blood pressure suffer from hypertension. Data on fasting blood sugar (milligrams/deciliter) and magnesium (milligrams/deciliter) in blood specimens collected from 60 patients diagnosed with hypertension were collected. The accompanying technology printout gives 90% confidence intervals for the mean fasting blood sugar (FBS) and mean magnesium level (MAG). Use this information to complete parts a through d below. Variable FBS MAG N 60 60 Mean 102.11 1.85238 StDev 38.91 0.05472 90% CI SE Mean 5.02 ( 93.72, 110.50 ) 0.00706 (1.84058, 1.86418) a. Locate and interpret the 90% confidence interval for mean fasting blood sugar on the printout. (Type integers or decimals. Do not round.) O A. The 90% confidence interval for mean fasting blood sugar indicates that 90% of all hypertensive patients will have a fasting blood sugar level between O B. The 90% confidence interval for mean fasting blood sugar indicates that 90% of hypertensive patients in the sample had a fasting blood…
1 (a) The amount of carbon monoxide in the daily emissions to outdoor has a normal distribution with a mean of 90 and a standard deviation of 20. For a random sample of 40 days, find the probability that the average amount of carbon monoxide emissions will exceed 80. (b) A researcher studied the tensile yield strength of steel. She performed tests on 20 steel samples and obtained a mean (X) of 305 MPa with a standard deviation (s) of 16 MPa. Based on her research, she claimed that the tensile yield strength of steel generally exceeds 300 MPa. Construct a 95% confidence interval for the population mean, assuming that the population is normally distribute (c) A traffic safety researcher obtained speed data of light and heavy vehicles travelling on a highway segment (refer Table (.1(c). He hypothesised that light vehicles travel at higher speeds than heavy vehicles. At the 0.05 significance level, can we conclude that light vehicles travel at higher speeds than heavy vehicles?
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For mated pairs of gallinules (type of water bird), let X equal the weight in grams of the male and Y the weight in grams of the female. Assume that X and Y have a bivariate normal distribution with #x = 415, o = 611, y = 347 and o=689. The correlation coefficient between X and Y is p = -0.25. (b) Determine the marginal distributions of X and then of Y. (c) Find the conditional distribution of Y|X = x. (d) Find E(Y|X = z) and Var(Y|X = x).
A population is distributed with a known standard deviation, σ = 18 units. A random sample of size 35 is obtained from this population. The mean of this sample is 70. True or False: Since the sample size is greater than 25 the distribution of sample means from this population should be approximately normally distributed. What is the lower limit of the 95% confidence interval for the population mean μ? (2 dp) What is the upper limit of the 95% confidence interval for the population mean μ? (2 dp). Based on your confidence interval, would you believe that the true mean of this population could be 75?
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A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of randomly selecting a score GREATER than 51? A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of selecting a sample of n = 4 scores with a mean more than M = 51? A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of selecting a sample of n = 36 scores with a mean more than M = 51?
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Vehicle speeds at a certain highway location are believed to have approximately a normal distribution with mean µ = 50 mph and standard deviation σ = 5 mph. The speeds for a randomly selected sample of n = 25 vehicles will be recorded. (a) Give numerical values for the mean and standard deviation of the sampling distribution of possible sample means for randomly selected samples of n = 25 from the population of vehicle speeds. Mean = s.d.(x) = (b) Use the Empirical Rule to find values that fill in the blanks in the following sentence. For a random sample of n = 25 vehicles, there is about a 95% chance that the mean vehicle speed in the sample will be between and mph. (c) Sample speeds for a random sample of 25 vehicles are measured at this location, and the sample mean is 59 mph. Given the answer to part (b), explain whether this result is consistent with the belief that the mean speed at this location is μ = 50 mph. A sample mean of 59 mph (when n = 25) --Select--- be consistent with…
Data taken from a sample of 25 LED lamps, a sample average of 2 years was obtained and a standard deviation of s=0.4 years. The estimator of the mean of lifetime of LED lamps at the confidence level/coefficient (1-α) is (2 ± 0.05 talpha/2 , where talpha/2 is the value of t in the t distribution with v=24) (2 ± 0.10 talpha/2 , where talpha/2 is the value of t in the t distribution with v=24) (2 ± 0.08 talpha/2 , where talpha/2 is the value of t in the t distribution with v=24 (other)

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