4. Suppose X1,... , Xn is a random sample of size n drawn from a Poisson pdf where A is an unknown parameter. Show X X is an unbiased estimator for X
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- Q1. Altitude and Temperature:Altitude( thousands of feet)3 10 14 22 28 31 33Temperature( 0?)57 37 24 −5 −30 −41 −54At 6.327 thousand feet, the author recorded the temperature. Find the best predicted temperatureat that altitude. How does the result compare to the actual recorded value of 480?? a) Find the value of the linear correlation coefficient ?b) Find the critical values of r from table A-6 using ∝= 0.05c) Determine whether there is sufficient evidence to support a claim of a linear correlationBetween the two variables.d) Find the regression equation,e) Letting the first variable be the predictor (x) variable, find the indicated predicted value.A company manufactures tonnis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.7 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between -to ak and t as then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.8 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -th os and to 96- -to.96 = 0.96 = (Round to three decimal places as needed.)A professor grades on a curve by assigning C's to all scores from u- ; to u+%, B's to all scores from i+% to µ+ , and D's to all scores from u – * to µ – 5. Everyone who scores below a D gets an F, and everyone who scores above a B gets an A. a. If the scores are normally distributed with mean u and variance o², what percentage of students will receive each grade? Hint: convert to z-scores and use pnorm() to find probabilities (percentages) b. If the scores are uniformly distributed (continuous) from 0 to 100 what percentage will receive each grade? Hint: first determine the values of u and o for this distribution
- Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175Please answer all bitsShow that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter 0.
- An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @Q.No.1. (Marks 08) Explain the following with suitable examples. Mutually exclusive events Sampling Correlation RegressionLet X1, X2,..., Xn be a random sample of size n > 3 from a normal distribution with unknown mean μ and known variance equal to 2. Show that is an unbiased estimator of μ and compute its variance. p
- Consider data 5,1,3,5,5,4,3,2 of the Poisson distribution with expectation u. We want to test H0:u=u0 with u0=2. Write the log-likelihood for the data under H0 and the likelihood ratio A(y) for testing H0e 14-25. A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1-5. Calculate the proportion of days on which (i) Neither car is used (ii) Some demand is refused.The data shown in the table represent the measurements of 10-kΩ resistors (in kΩ) produced from five different machines. A random sample of nine resistors from each machine is taken to determine whether the mean resistance varies from one machine to another. Perform analysis of variance and test the hypothesis at the 0.05 level of significance that the mean resistances differ significantly for the five machines, all through manual computations. Show all complete and systematic solutions.
