The amount filled (Y) by a certain bottling machine is a random variable that follows a...
8.40
stion 4 (6 pt) (Ex. 8.40 on page 409 is modified): Suppose that random variable Y is an observation from a normal distribution with unknown mean u and variance l Find and verify a pivotal quantity that you can use to derive confidence limits for the mean u. Find a 95% lower confidence limit for. a. b. 8.40 Suppose that the random variable Yis an observation from a normal distribution with unknown mean μ and variance 1 . Find...
3. Suppose that the length of iron rods from a certain factory follows the normal distribution with known standard deviation o = 0.2 m but unknown mean u. Construct a 88% confidence interval for the population mean u if a random sample of n = 16 of these iron rods has sample mean of 6 m. Z= E = CI:
6. Let Xi 1,... ,Xn be a random sample from a normal distribution with mean u and variance ơ2 which are both unknown. (a) Given observations xi, ,Xn, one would like to obtain a (1-a) x 100% one-sided confidence interval for u as a form of L E (-00, u) the expression of u for any a and n. (b) Based on part (a), use the duality between confidence interval and hypothesis testing problem, find a critical region of size...
Suppose that the weekly amount of down time in hours, Y, for an industrial machine follows a Gamma distribution with mean lb = aß = 2ß, where B is an unknown parameter. The weekly loss in dollars, X, to the industrial operation as a result of this down time is given by X = 3Y + 30. Based on a sample of n observations, find an unbiased estimator for of as a function of the statistic y.
Let Ybe a normal random variable with parameters (1,a2). In other words, its mean is 1 while its variance a2 is unknown. Find 95% upper one-sided confidence interval for a2 in terms of Y
Let Ybe a normal random variable with parameters (1,a2). In other words, its mean is 1 while its variance a2 is unknown. Find 95% upper one-sided confidence interval for a2 in terms of Y
4. Let X be a random variable with pdf f(x). Suppose that the mean of X is 2 and the variance of X is 5. It is easy to show that the pdf of Y = 0X is fo(y) = f(1/0) (You do not have to show this, but it's good practice.) Suppose the popula- tion has the distribution of foly) with 8 unknown. We take a random sample {Y}}=1 and compute the sample mean Y. (a) What is a...
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by C 3Y2. If Y, Y2, Y denote the observed number of breakdowns for n independently selected days, find an MVUE for E(C).
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by...
2. Let u be the mileage of a certain brand of tire. A sample of n = 20 tires is taken at random, resulting in the sample mean X = 32, 215 and sample variance s2 = 3, 116. Assuming that the distribution is normal, find a 99 percent confidence interval for u.
3. Let X be normal random variable and Y be a Chi-square random variable with df degrees of freedom then the ratio follows (note that this is the reason we use a common test when We don't know for certain the true value of the variance): a) A x?distribution b) A normal distribution c) An F distribution d) At distribution.
A soda bottling plant fills cans labeled to contain 12 ounces of
soda. The filling machine varies and does not fill each can with
exactly 12 ounces. To determine if the filling machine needs
adjustment, each day the quality control manager measures the
amount of soda per can for a random sample of 50 cans. Experience
shows that its filling machines have a known population standard
deviation of 0.35 ounces.
In today's sample of 50 cans of soda, the sample...