Consider a random sample of n independent Xi's that was drawn from a population with mean ux and variance σ².
a) Find the expected value of the total, S = Σ (n i=1) Xi
b) Find the variance of the Total S= (n i=1) Xi
c) If ux = 10, σ² = 20 and n = 10, calculate the numerical values found in a, b
d) Did a, b or both require that the random variables were independent? Explain
Consider a random sample of n independent Xi's that was drawn from a population with mean...
A random sample of n=7 observations are drawn from a normal population with mean and variance σ^2. The mean and variance of the sample are 1.45 and 2.07 respectively. Calculate a 90% confidence interval for the population standard deviation.
1. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and variance σχ2. Assume that n 2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes x] and x2. Let estimate f x of true mean ux be μΧ-(X1 + x2)/2. Then the random variable associated with estimate Axis estimator Ax- (XI...
Let X_1,X_2,……… X_10 be an independent random sample of size n=10 from a population having mean μ=8 and variance σ^2=4. Consider the following estimators of μ: μ ̂_1=X ̅ and μ ̂_2=2X_1-X_2. Check unbiasedness of above estimators. If biased find the amount of bias. Determine the variance of the estimators. Find the relative efficiency and identify the best estimators.
Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random variables with mhean μ and variance a) Compute the expected value of W b) For what value of a is the variance of W a minimum? σ: Let W-aX + (1-a) Y, where 0 < a < 1. Let Xi, x,, ,X, be independent random variables with mean and variance σ . Let Y1-Y2, , Y, be independent random...
Consider a random experiment that has as an outcome the number x. Let the associated variable be X, with true (population) and unknown probability density function fx(x), mean ux. and variance σχ2. Assume that n-2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes xi and x2 Let estimate μ X of true mean #xbe μχ = (x1+x2)/2. Then the random variable associated with estimate μ xis estimator random 1. a. Show the...
simple random sample of size n= 40 is drawn from a population. The sample mean is found population mean. be x 120.6 and the sample standard deviation is found to be s 12.6. Construct a 99% confidence interval for the The lower bound is (Round to two decimal places as needed.)
A simple random sample of size n = 20 is drawn from a population that is normally distributed. The sample mean is found to be x = 66 and the sample standard deviation is found to be s = 10. Construct a 90% confidence interval about the population mean.
A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x overbar equals 120.7 and the sample standard deviation is found to be s=12.1. Construct a 99% confidence interval for the population mean. The lower bound is ________ (Round to two decimal places as needed.) The upper bound is ________ (Round to two decimal places as needed.)
A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x overbar equals 120.7 and the sample standard deviation is found to be s=12.1. Construct a 99% confidence interval for the population mean. The lower bound is ________ (Round to two decimal places as needed.) The upper bound is ________ (Round to two decimal places as needed.)
A simple random sample of size n 40 is drawn from a population. The sample mean is found to be x 120.1 and the sample standand deviation is found to be s 12.4 Construct a 99% conidence interval for the populaton mean The lower bound is (Round to two decimal places as needed) The upper bound is (Round to two decimel places as needed.)