Question

You have an observation x from N(o,σ). Decide c so that c|x| is a unbiased estimation...

You have an observation x from N(o,σ). Decide c so that c|x| is a unbiased estimation of σ and calculate the estimations variance. Answer exactly.

please explain thoroughly.
thank you in advance. :)

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Given,

where x is a single observation from the normal population

To find,
An unbiased estimator of using x

we know,

the unbiased estimator of is,
                                                       

we know that the mean of the population is 0,

thus an unbiased estimator of ,
                                                       

Checking,


                

Required which would be the unbiased estimator of .

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Which of the following will have the largest intermolecular attractiveness? Please explain. H-F, P-N, C-Si, O-O
Which of the following will have the largest intermolecular attractiveness? Please explain. H-F, P-N, C-Si, O-O
Let X1, X2,...,Xn represent n random draws from a population with standard deviation σ and variance...
Let X1, X2,...,Xn represent n random draws from a population with standard deviation σ and variance σ^2 , so that V ar[X1] = V ar[X2] = ... = V ar[Xn] = σ^ 2 . Define the sample average taken from a sample of size n as follows: X¯ n ≡ (X1 + X2 + ... + Xn)/ n . a) Derive an expression for the standard deviation of X¯ n. [Hint: Your answer should depend only on σ and n]...
If the critical angle for light going from material X into water (n=1.33) is (32.0+C)o ,...
If the critical angle for light going from material X into water (n=1.33) is (32.0+C)o , what is the index of refraction for material X? Give your answer with 3 significant figures. C= 6 Consider a ray of white light incident from the air on a dispersive material at an angle of incidence of (42.5+A)o. The red light refracts to an angle of (29.5+B)o in the dispersive material. If the index of refraction for green light is 7.50% larger than...
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 the following hypotheses: H0: µ = 2 vs Ha: µ ≠ 2, and σ =...
Suppose the following hypotheses: H0: µ = 2 vs Ha: µ ≠ 2, and σ = 20, sample mean = 12, and use alpha = 0.05 a.     If n = 10 what is p-value? b.     If n = 15, what is p-value? c.     If n = 20 what is p-value? d.     Summarize your findings from above. Please show your work and thank you SO much in advance! You are helping a struggling stats student SO much!
Summation from n=2 to infinity of ln(n)/n^2 * x^n a.) Let x=-1, and compute the integral...
Summation from n=2 to infinity of ln(n)/n^2 * x^n a.) Let x=-1, and compute the integral test to determine whether this it is convergent or divergent b.) Compute the ratio test to determine the interval of convergence and explain what this interval represents. I'm really confused with this problem (specifically a)- please write out all of the details of computing the integral so I can understand. Thank you!
An independent-measures study with n = 8 in each treatment produces M = 75 for the...
An independent-measures study with n = 8 in each treatment produces M = 75 for the first treatment and M = 71 for the second treatment with a pooled variance of 9. Construct a 95% confidence interval for the population mean difference. Can you please show the work thoroughly, I have the answer, which is 0.7825<x<7.2175, I just need help in how to get to the answer. Thank you!
A sample of n=14 observations is drawn from a normal population with μ=1030 and σ=200. Find...
A sample of n=14 observations is drawn from a normal population with μ=1030 and σ=200. Find each of the following: A. P(X¯>1110) Probability = B. P(X¯<944) Probability = C. P(X¯>997) Probability = THANK YOU!!
Assume that X ∼ N(μ,σ). For each of the following, the generic number c is a...
Assume that X ∼ N(μ,σ). For each of the following, the generic number c is a number bigger than μ. (a) Write down the statement: “What is the probability that X is greater than c?” using P ( ) notation. Draw a picture of shaded curve. (b) Rewrite A) by standardizing X (turning it into Z). Hint: you will still have μ, σ, and c in the expression (c) Redo questions (a) and (b) for the statement: “What is the...
Suppose the random variable X follows the Poisson P(m) PDF, and that you have a random...
Suppose the random variable X follows the Poisson P(m) PDF, and that you have a random sample X1, X2,...,Xn from it. (a)What is the Cramer-Rao Lower Bound on the variance of any unbiased estimator of the parameter m? (b) What is the maximum likelihood estimator ofm?(c) Does the variance of the MLE achieve the CRLB for all n?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT