Question

Choose the all correct things Sn=X1+X2+...+Xn 1. E[Sn]=2n, when RV X1,...,Xn is iid and E[X]=2 2....

Choose the all correct things

Sn=X1+X2+...+Xn

1. E[Sn]=2n, when RV X1,...,Xn is iid and E[X]=2

2. VAR[Sn]=3n, when RV X1,...,Xn is iid and VAR[X]=3

3. VAR[Sn]=2n is always correct, when RV X1,...,Xn is identically distributed and VAR[X]=2

4 .Sn is an Exponential distribution with a mean of 2n and a variance of 3n ,when RV X1,...,Xn is iid and E[X]=2, VAR[X]=3 Exponential distribution

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

Homework Answers

Answer #1

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
Let X1, X2, . . . , Xn be iid following exponential distribution with parameter λ...
Let X1, X2, . . . , Xn be iid following exponential distribution with parameter λ whose pdf is f(x|λ) = λ^(−1) exp(− x/λ), x > 0, λ > 0. (a) With X(1) = min{X1, . . . , Xn}, find an unbiased estimator of λ, denoted it by λ(hat). (b) Use Lehmann-Shceffee to show that ∑ Xi/n is the UMVUE of λ. (c) By the definition of completeness of ∑ Xi or other tool(s), show that E(λ(hat) |  ∑ Xi)...
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)...
X1 and X2 are iid exponential (2) random variables and Z=max(X1 , X2). What is E[Z]?...
X1 and X2 are iid exponential (2) random variables and Z=max(X1 , X2). What is E[Z]? (Hint: Find CDF and then PDF of Z) A. 3/2 B. 3 C. 1/2 D. 3/4
let X1 X2 ...Xn-1 Xn be independent exponentially distributed variables with mean beta a). find sampling...
let X1 X2 ...Xn-1 Xn be independent exponentially distributed variables with mean beta a). find sampling distribution of the first order statistic b). Is this an exponential distribution if yes why c). If n=5 and beta=2 then find P(Y1<=3.6) d). find the probability distribution of Y1=max(X1, X2, ..., Xn)
Problem 1 Let X1, · · · , Xn IID∼ p(x; θ) = 1/2 (1 +θx),...
Problem 1 Let X1, · · · , Xn IID∼ p(x; θ) = 1/2 (1 +θx), −1 < x < 1, −1 < θ < 1. 1. Estimate θ using the method of moments. 2. Show that the above MoM is consistent by showing it’s mean square error converges to 0 as n goes to infinity. 3. Find its asymptotic distribution.
A random sample X1, X2, . . . , Xn is drawn from a population with...
A random sample X1, X2, . . . , Xn is drawn from a population with pdf. f(x; β) = (3x^2)/(β^3) , 0 ≤ x ≤ β 0, otherwise (a) [6] Find the pdf of Yn, the nth order statistic of the sample. (b) [4] Find E[Yn]. (c) [4] Find Var[Yn]. (d)[3] Find the mean squared error of Yn when Yn is used as a point estimator for β (e) [2] Find an unbiased estimator for β.
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α]...
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α. (a) Derive the cumulative distribution function...
5. Consider a simple case with only four independently and identically distributed (iid) observations, X1, X2,...
5. Consider a simple case with only four independently and identically distributed (iid) observations, X1, X2, X3, X4, on a random variable X. Consider these two estimators: µˆ1 = 1/12 (2X1 + 4X2 + 4X3 + 2X4), µˆ2 = 1/12 (X1 + 5X2 + 5X3 + X4). a Show that each is unbiased, and that one is more efficient than the other. b Show that the usual sample mean is more efficient than either. Explain why the others given above...
Let X1,…, Xn be a sample of iid Exp(?1, ?2) random variables with common pdf f...
Let X1,…, Xn be a sample of iid Exp(?1, ?2) random variables with common pdf f (x; ?1, ?2) = (1/?1)e−(x−?2)/?1 for x > ?2 and Θ = ℝ × ℝ+. a) Show that S = (X(1), ∑ni=1 Xi ) is jointly sufficient for (?1, ?2). b) Determine the pdf of X(1). c) Determine E[X(1)]. d) Determine E[X2(1) ]. e ) Is X(1) an MSE-consistent estimator of ?2? f) Given S = (X(1), ∑ni=1 Xi )is a complete sufficient statistic...
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT