Question

X1 is normal with mean mu and variance sigma^2. X2 is normal with mean mu and...

X1 is normal with mean mu and variance sigma^2. X2 is normal with mean mu and variance 2sigma^2. Consider the estimator cX1 + (1-c)X2. For what value of c is the variance minimized?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Y = constant X1,X2,X3~N(mu,sigma^2) P(X1>Y AND X1+X2>2Y AND X1+X2+X3>3Y) = ?
Y = constant X1,X2,X3~N(mu,sigma^2) P(X1>Y AND X1+X2>2Y AND X1+X2+X3>3Y) = ?
Suppose X1 is from a population with mean µ and variance 1 and X2 is from...
Suppose X1 is from a population with mean µ and variance 1 and X2 is from a population with mean µ and variance 4 (X1, X2 are independent). Construct an estimator of ? as ?̂=??1+(1−?)?2. Show that ?̂ is unbiased for ?. Find the most efficient estimator in this class, that is, find the value of a such that the estimator has the smallest variance.
Suppose X1 is from a population with mean µ and variance 1 and X2 is from...
Suppose X1 is from a population with mean µ and variance 1 and X2 is from a population with mean µ and variance 4 (X1, X2 are independent). Construct an estimator of ? as ?̂=??1+(1−?)?2. Show that ?̂ is unbiased for ?. Find the most efficient estimator in this class, that is, find the value of a such that the estimator has the smallest variance.
Let X1, X2, X3, and X4 be a random sample of observations from a population with...
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: 1 = 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4. Is this a biased estimator for the mean? What is the variance of the estimator? Can you find a more efficient estimator?) ( 10 Marks)
The random variables X1 and X2 both follow normal distributions. The mean of X1 is E(X1)=5,...
The random variables X1 and X2 both follow normal distributions. The mean of X1 is E(X1)=5, and its variance is V(X1)=2 The mean of X2 is E(X2)=9, and its variance is V(X2)=3. If Y is a random variable such that Y = 3X1+5X2, what is P(Y<70)? A student takes 4 measurements and finds that the mean is 64 and the sample variance is 81. What is the sample standard deviation For a random variable X, which statement is most likely...
Let X1, X2 be two normal random variables each with population mean µ and population variance...
Let X1, X2 be two normal random variables each with population mean µ and population variance σ2. Let σ12 denote the covariance between X1 and X2 and let ¯ X denote the sample mean of X1 and X2. (a) List the condition that needs to be satisfied in order for ¯ X to be an unbiased estimate of µ. (b) [3] As carefully as you can, without skipping steps, show that both X1 and ¯ X are unbiased estimators of...
Consider a large population which has population mean µ, and population variance σ 2 . We...
Consider a large population which has population mean µ, and population variance σ 2 . We take a sample of size n = 3 from this population, thinking of the samples as realizations of the RVs X1, X2, and X3, where the Xi can be considered iid. We are interested in estimating µ. (a) Consider the estimator ˆµ1 = X1 + X2 − X3. Is this estimator unbiased for µ? Explain your answer. (b) Find the variance of ˆµ1. (c)...
Suppose that X1 and X2 are independent standard normal random variables. Show that Z = X1...
Suppose that X1 and X2 are independent standard normal random variables. Show that Z = X1 + X2 is a normal random variable with mean 0 and variance 2.
Let X1, X2, . . . , Xn be iid exponential random variables with unknown mean...
Let X1, X2, . . . , Xn be iid exponential random variables with unknown mean β. (1) Find the maximum likelihood estimator of β. (2) Determine whether the maximum likelihood estimator is unbiased for β. (3) Find the mean squared error of the maximum likelihood estimator of β. (4) Find the Cramer-Rao lower bound for the variances of unbiased estimators of β. (5) What is the UMVUE (uniformly minimum variance unbiased estimator) of β? What is your reason? (6)...
Let X1,X2...Xn be i.i.d. with N(theta, 1) a) find the CR Rao lower-band for the variance...
Let X1,X2...Xn be i.i.d. with N(theta, 1) a) find the CR Rao lower-band for the variance of an unbiased  estimator of theta b)------------------------------------of theta^2 c)-----------------------------------of P(X>0)