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Suppose that the weekly amount of down time in hours, Y, for an industrial machine follows...
QUESTION 3 Suppose that Y, Y2, ., Y, are independent variables such that Y, =Bx? +€,,...
QUESTION 3 Suppose that Y, Y2, ., Y, are independent variables such that Y, =Bx? +€,, != 1,2,,n, where B is an unknown parameter, X1, X2, X, are known real numbers (+0), and €1. €2. ,€, are independent random errors each with a normal distribution with mean 0 and variance o (a) Show that is an unbiased estimator of B What is the variance of the estimator? (b) Show that the least squares estimator of B is not the same...
The amount filled (Y) by a certain bottling machine is a random variable that follows a...
The amount filled (Y) by a certain bottling machine is a random variable that follows a Normal distribution with unknown mean and unknown variance. Based on a sample of n=19, the two-sided 98% confidence for u, is (8.72, 10.63). What are the values of the sample mean and sample variance?
Show all working clearly. Thank you. 1. In this question, X is a continuous random variable...
Show all working clearly. Thank you.
1. In this question, X is a continuous random variable with density function (x)a otherwise where ? is an unknown parameter which is strictly positive. You wish to estimate ? using observations X1 , . …x" of an independent random sample XI…·X" from X Write down the likelihood function L(a), simplifying your answer as much as possi- ble 2 marks] i) Show that the derivative of the log likelihood function (a) is 4 marks]...
3. Suppose that the 5-year survival probability, X, for women with breast cancer who live in...
3. Suppose that the 5-year survival probability, X, for women with breast cancer who live in a rural county follows Beta distribution with probability density function (pdf) fx (20) = 0.00-1 where 0 < x < 1 and parameter 6 > 0. Let X1, ..., X, be a random sample of size n from a population of rural counties. Researchers intend to make statistical inference on the parameter 6 using collected data X1, ..., (a) Let Y; = – log(Xi)...
During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down...
During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with a 1 and B 2. That is, 2(1 - y), 0s ys 1, f(y) lo, elsewhere. The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by C your answers to two decimal places.) 50Y 2y. Find the mean and variance of C. (Round...
7. Suppose that waiting time, Y, at a particular restaurant follows an Exponential distribution with mean...
7. Suppose that waiting time, Y, at a particular restaurant follows an Exponential distribution with mean X, where X is a Geometric random variable with mean 1/ p. Find the unconditional mean and variance of Y.
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson...
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 3 breakdowns every 588 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find and ux. (Write the fraction in reduced form.) = My = (b) Write the formula for the exponential probability curve of x. f(x) = 1 e-x/ for x 2 (d) Assuming that the maintenance department's claim is true, find...
The maintenance department in a factory claims that the number of breakdowns of a particular machine...
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 4 breakdowns every 384 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and μx. (Write the fraction in reduced form.) (b) Write the formula for the exponential probability curve of x. (d) Assuming that the maintenance department's claim is true, find the probability that the time between successive breakdowns is...
Return to the original model. We now introduce a Poisson intensity parameter X for every time point and denote the parameter () that gives the canonical exponential family representation as above by...
Return to the original model. We now introduce a Poisson intensity parameter X for every time point and denote the parameter () that gives the canonical exponential family representation as above by θ, . We choose to employ a linear model connecting the time points t with the canonical parameter of the Poisson distribution above, i.e., n other words, we choose a generalized linear model with Poisson distribution and its canonical link function. That also means that conditioned on t,...
Consider the following point estimators, W, X, Y, and Z of μ: W = (x1 +...
Consider the following point estimators, W, X, Y, and Z of μ: W = (x1 + x2)/2; X = (2x1 + x2)/3; Y = (x1 + 3x2)/4; and Z = (2x1 + 3x2)/5. Assuming that x1 and x2 have both been drawn independently from a population with mean μ and variance σ2 then which of the following is true...Which of the following point estimators is the most efficient? A. Z B. W C. X D. Y An estimator is unbiased...
QUESTION 3 Suppose that Y, Y2, ., Y, are independent variables such that Y, =Bx? +€,, != 1,2,,n, where B is an unknown parameter, X1, X2, X, are known real numbers (+0), and €1. €2. ,€, are independent random errors each with a normal distribution with mean 0 and variance o (a) Show that is an unbiased estimator of B What is the variance of the estimator? (b) Show that the least squares estimator of B is not the same...
The amount filled (Y) by a certain bottling machine is a random variable that follows a Normal distribution with unknown mean and unknown variance. Based on a sample of n=19, the two-sided 98% confidence for u, is (8.72, 10.63). What are the values of the sample mean and sample variance?
Show all working clearly. Thank you.
1. In this question, X is a continuous random variable with density function (x)a otherwise where ? is an unknown parameter which is strictly positive. You wish to estimate ? using observations X1 , . …x" of an independent random sample XI…·X" from X Write down the likelihood function L(a), simplifying your answer as much as possi- ble 2 marks] i) Show that the derivative of the log likelihood function (a) is 4 marks]...
3. Suppose that the 5-year survival probability, X, for women with breast cancer who live in a rural county follows Beta distribution with probability density function (pdf) fx (20) = 0.00-1 where 0 < x < 1 and parameter 6 > 0. Let X1, ..., X, be a random sample of size n from a population of rural counties. Researchers intend to make statistical inference on the parameter 6 using collected data X1, ..., (a) Let Y; = – log(Xi)...
During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with a 1 and B 2. That is, 2(1 - y), 0s ys 1, f(y) lo, elsewhere. The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by C your answers to two decimal places.) 50Y 2y. Find the mean and variance of C. (Round...
7. Suppose that waiting time, Y, at a particular restaurant follows an Exponential distribution with mean X, where X is a Geometric random variable with mean 1/ p. Find the unconditional mean and variance of Y.
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 3 breakdowns every 588 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find and ux. (Write the fraction in reduced form.) = My = (b) Write the formula for the exponential probability curve of x. f(x) = 1 e-x/ for x 2 (d) Assuming that the maintenance department's claim is true, find...
Return to the original model. We now introduce a Poisson intensity parameter X for every time point and denote the parameter () that gives the canonical exponential family representation as above by θ, . We choose to employ a linear model connecting the time points t with the canonical parameter of the Poisson distribution above, i.e., n other words, we choose a generalized linear model with Poisson distribution and its canonical link function. That also means that conditioned on t,...
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