show that ∑Xi is a sufficient statistic for l.
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Let X1, . . ., Xn be a random sample of component
lifetimes from an exponential distribution with
parameter l. Use the factorization theorem to
show that ∑Xi is a sufficient statistic for l.
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- From a population of 4 students, a random variable (X) is measured in terms of age and the values of X are 24, 20, 22, 18. Find the sampling distribution where n = 1 Compute for the Variance when n=1a) Find such that P( X < ? ) = 0.9332, where X is a normal random variable with mean = 10 and standard deviation = 2.5. b) Find such that P( X > ?) = 0.1230, where X is a normal random variable with mean = 10 and standard deviation = 2.5.A simple random sample without replacement was used to select 5 clusters from a population of 29 clusters. From each selected sample cluster simple random sampling without replacement was used to select samples of secondary units. For this data find an estimate of the population total and the population mean along with their estimated variances. clmemb clsize yval [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,] [21,] [22,] [23,] [24,] [25,] [26,] [27,] [28,] [29,] [30,] [31,] [32,] [33,] 1 20 46.07 20 45.54 20 43.07 1 1. 1 20 49.29 1 20 44.35 1 20 45.21 2 33 44.11 2 33 42.19 2 33 44.42 2 33 40.05 2 33 43.88 2 33 47.45 2 33 40.41 2 33 43.24 3 22 35.42 3 22 35.46 3 22 36.34 3 22 35.25 4 40 38.67 4 40 34.73 4 40 39.28 4 40 35.26 4 40 39.84 4 40 40.32 4 40 40.03 4 40 38.15 4 40 38.69 4 40 39.38 18 47.48 18 44.78 5 18 44.37 18 44.97 5 18 49.20
- A company claims that the number of defective items manufactured during each run of making 100 of their products is independent of the number from other runs and that the proportion of defectives is not more than 3%. Assuming that the defective rate for each run is 3% Which of the following can be used to determine whether x = 8 is unusually a high number of defective items on the next run of 100 of their products?x; Let be a random variable from the normal distribution with 8 means, 16 variances.Let's select a subset of 25 elements from the main massthe mean of these subsets MUST BE BETWEEN 7 and 10.An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places
- Let x be a random variable that represents the weight of a lion in a certain region of Africa. Assume that x is normally distributed with a mean = 260 lbs . With standard deviation =30 lb Please include the graphs for questions A and BLet X,, X,, .., X, (n>3) be a random sample from a normal distribution with mean µ and variance o', both unknown. a) Find complete sufficient statistics for (u,o²) hence determine the UMVUE of 4, b) If in part (a) the variance o² =1, then give a UMVUE for u'. Justify your answer. %3DIf continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?
- 2. Cytomegalovirus (CMV) is a (generally benign) virus that infects one – half of young adults. If a random sample of 10 young adults is taken, find the probability that between 30% and 40% (inclusive) of those sampled will have CMV. Use the normal approximation with the continuity correction.200 poodles 61 are left-paued left -pawed. a random sample of In a random sample ef 220 labradores 38 are Can we conclude that the difference in The tuo sample proportions of left pawed dogs is statistically significont for x= 0.05 ?The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs. d) About how many of the 81 sampled home runs have length between 400 and 420 feet? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot?
