(16 points) Suppose the breaking strength of plastic bags is a Gaussian random variable Bags from company i have a mean strength of 8 kilograms and a variance of 1 kg2; Bags from company 2 have a...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
11. (16 pts) Suppose that the mean time from the date of service to the date of payment for one insurance company was 41.4 days last year. To estimate the mean time this year, a sample of 50 claims is selected. The sample mean time from the date of service to the date of payment was = 38.2 days. Suppose the population standard deviation was σ = 7.4 days. (a) What is the population? What is the sample? (b) At...
24. If the population mean is 0 and the population variance o, 1 (10 points) What is the P (z> 3) a. What is the P (z<2) b. What is the P (-1.5<z <3)? c. What is the P (-2.33cz < 1.25)? d. e. What is the P (-2.33<z and >1.25)? 25. If the population mean is 115 and the population variance σ, 100 (10 points) What is the P (z > 120) a. b. What is the P (2<150)?...
2. (10pts) The following 16 random samples; 5.33, 4.25, 3.15, 3.70, 1.61, 6.40, 3.12, 6.59,3.53, 4.74, 0.11, 1.60, 5.49, 1.72, 4.15, 2.30, came from normal distribution with mean μ and variance σ2, i.e., Xi, X2' .. . , X16 ~ N(μ, σ*), with the density function (a) (4pts) Find the maximum likelihood estimates of μ and σ2, denoted with μ and σ2. (b) (4pts) Based on above μ and σ2, construct 95% confidence intervals for μ and σ2 separately. (c)...
I. Suppose we have a simple random sample from x,, , x, which have mean μ-E(X) and variance = tar Find (a) E ((X-μ)2 (d) E ((X-μ)2), where 1--ΣΧ, I. Suppose we have a simple random sample from x,, , x, which have mean μ-E(X) and variance = tar Find (a) E ((X-μ)2 (d) E ((X-μ)2), where 1--ΣΧ,
(7 pts) From previous studies, it has been generally believed that Northern Hemisphere icebergs have a mean depth of 270 meters and a standard deviation of 20 meters. An environmentalist has suggested that global warming has caused icebergs to have greater depth. A team of scientists visiting the Northern Hemisphere observed a random sample of 41 icebergs. The depth of the base of the iceberg below the surface was carefully measured for each and the sample mean and standard deviation...
7 points) From previous studies, it has been generally believed that Northern Hemisphere icebergs have a mean depth of 270 meters and a standard deviation of 20 meters. An environmental ist has suggested that global warming has caused icebergs to have greater depth. A team of scientists visiting the Northern Hemisphere observed a random sample of 41 icebergs. The depth of the base of the iceberg below the surface was carefully measured for each and the sample mean and standard...