Stats and probability Let X denote the proportion of allotted time that a randomly selected student spendsworking on a certain aptitude test. Suppose the pdf of X isf(x; 0) = {(0+1)x0, 0≤x≤10, otherwisewhere -1< 0. A random sample of ten students yields data x₁ = 0.92, x2 = 0.79, x3 = 0.90,x4 = 0.65, x5 = 0.86, x6 = 0.47, x7 = 0.73, x8 = 0.97, x9= 0.94, x10 = 0.77.(a)(b)Use the method of moments to obtain an estimator of 0, and then compute theestimate for this data.Obtain the maximum likelihood estimator of 0, and then compute theestimate for the given data.35.923NOVzoom18##PחיC$G4RMacBook ProG Search or type URL%0056>&87☆WTYU890100

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Answered: Let X denote the proportion of allotted…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 4ECP

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Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = (0+1)x where -1 < 0. A random sample of ten students yields data x₁ = 0.86, x₂ = 0.92, x3 = 0.95, x4 = 0.94, X5 = 0.45, x6 = 0.65, x = 0.73, xg = 0.90, x9 = 0.79, X10 = 0.79. (a) Use the method of moments to obtain an estimator of Ⓒ 1 (1 + X) - 1 1 0 (x - 1) - - 2 0 (1-7) - -n ΣIn(X) Eln(X;) n 2 0 (1 + 7) 1 0 (7-1) - Compute the estimate for this data. (Round your answer to two decimal places.) 0≤x≤ 1 otherwise 1 (b) Obtain the maximum likelihood estimator of 0. Eln(X;) n ΣΙn(Χ;) -n - 1 1 n ΣIn(Χ.) Compute the estimate for the given data. (Round your answer to two decimal places.)
Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of Xis F(x; 6) = 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = 0.65, x₂ = 0.92, x₁=0.86, x40.94, X-0.95, x=0.73, x=0.90, X-0.49, x 0.79, *10= 0.79. (a) Use the method of moments to obtain an estimator of 1 O 0 (x-1)-2 0 (x-1)-1 O 0 (1+)-1 -2 Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. Lin(X)) n Zn(x)) -n -n Din(x) n in(X) ΣΟΧ) 1
A researcher believes at 49% of people who grew up as the only child have an IQ score over 100. However, unknown to the researcher this figure is actually 50% which is the same as the general population. To attempt to find evidence for the claim, the researcher is going to take a random sample of 400 people who grew up as an only child. Let X be the proportion of people in the sample with an IQ score above 100. (a) find the mean of C (b) find the standard deviation of X (c) compute the approximation for P(x >0.49) , which is the probability that there will be 49% or more with the IQ scores over 100 in the sample. Round your answer to four decimal places. * greater than sign, is supposed to be greater than or equal to sign*
27. Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = (0+1)xº 0≤x≤1 for some > -1. A random sample of ten students yields data x₁ = .92, x₂ = .79, X3 = .90, X4 = .65, x5 = .86, x6 = .47, X7 = .73, x8 = .97, x9 = .94, X10 = .77. a. Use the method of moments to obtain an estimator of 0, and then compute the estimate for this data. b. Obtain the maximum likelihood esti- mator of 0, and then compute the esti- mate for the given data.
Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 continuous hours. Following are the summary statistics: x = 14.5 hours, s = 1,2 hours
Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 8.4. Find the probability of no dandelions in an area of 1 m². P(X= 0) = Find the probability of at least one dandelion in an area of 1 m². P(at least one) = Find the probability of at most two dandelions in an area of 1 m². P(X ≤2) = Question Help: Message instructor Submit Question Jump to Answer
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following. 0.17e-0.17(x - 0.5) - {0.17e-0.1 x ≥ 0.5 otherwise (a) What is the probability that time headway is at most 6 sec? (Round your answer to three decimal places.) f(x) = (b) What is the probability that time headway is more than 6 sec? At least 6 sec? (Round your answers to three decimal places.) more than 6 sec at least 6 sec (c) What is the probability that time headway is between 5 and 6 sec? (Round your answer to three decimal places.)
Suppose that the 101 randomly selected eighth-grade students (mentioned in question 6) took a “practice” test similar to the official standardized test a month before the official test was administered. The researchers reported that the (two-tailed) statistical test of the difference between the practice and official test scores resulted in t100 = -2.32, p < .05. (a) Given that the difference score was computed as D = (practice score – official score), do the reported results indicate that students scored significantly higher or lower on the official test relative to the practice test? Explain. (b) If we constructed the corresponding 95% confidence interval for the mean difference (between the practice and official test scores) in the population, would it include zero? Explain.
CBS news reported that 4% of adult Americans have a food allergy consider selecting 10 adult Americans at random define the variable x as: x= number of people in the sample of 10 that have a food allergy a. p(x<3) b. p(x lesss than or equal to 3) c. p (x greater than or equal to 4) d. p (1 less than or equal to x less than or equal to 3)
'Time headway' in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) = {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?
Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is (0 + 1)xº 0 < x < 1 f(x; 0) otherwise where -1 < 0. A random sample of ten students yields data x, 0.99, x2 = 0.45, x3 = 0.94, x4 = 0.92, x5 = 0.79, x6 = 0.86, X7 0.73, xg = 0.90, X9 = 0.79, x10 = 0.65. %3D (a) Use the method of moments to obtain an estimator of 0 1 1 + X 1 - 2 1 - X 1 - 1 1 + X X - 1 1 - 1 1 Compute the estimate for this data. (Round your answer to two decimal places.)

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