Question: Suppose Y 1 ,Y 2 ,...,Yn is a random sample from the exponential pdf, f Y (y; ) = e y , y > 0.

Suppose Y1,Y2,...,Yn is a random sample from the exponential pdf, fY (y; λ) = λe−λy, y > 0.

(a) Show that λˆn = Y1 is not consistent for λ.

(b) Show that n n = ; = i=1 is not consistent for λ.

n n = ; = i=1

Step by Step Solution

★★★★★

3.51 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a To show that n Y1 is not consistent for we need to show that lim n Pn 0 for some 0 Since Y1 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Introduction To Mathematical Statistics Questions!

Q:

Suppose y 1 , y 2 , ..... y n is a random sample from a normal distribution with unknown mean m and variance 2 = 1, i.e., Show that the likelihood L of the sample is 1 f(y) %3D V27

Q:

Suppose that X1, X2., Xn is a random sample from a continuous probability distribution with median μ (a) Show that Hint: The complement of the event [min(Xi) (b) Write down a 100 (1 a) %...

Q:

Suppose that a random sample from a normal population with the known variance Ï2 is to be used to test the null hypothesis µ = µ0 against the alternative hypothesis µ =...

Q:

Suppose Y 1 , Y 2 , . . . , Y n is a random sample from the exponential pdf, f Y (y; ) = e y , y > 0. (a) Show that n = Y 1 is not consistent for . (b) Show that n = is not consistent for . . i=1

Q:

I would like to get the help from Question 1-12 Thanks for helping Directions: Submit solutions to the following problems in beginning of lecture on the due date. Make sure that your solutions are...

Q:

A) Suppose that a biased sample variance was defined as: $2 n+1 and that the true population variance is o?. Calculate the following ratio to 4 decimal places where n= 9 E(S;) 02 Hint: If S^2 is...

Q:

1. (a) Y1,Y2, ..., Yn form a random sample from a probability distribution with cumu- lative distribution function Fy(y) and probability density function fy(y). Let Y(1) = min{Y, Y2, ..., Yn}. Write...

Q:

Suppose Y1, Y2, . . . , Yn is a random sample from the uniform pdf over [0, 1]. The geometric mean of the numbers is the random variable nY1Y2 Yn. Compare the expected value of the geometric...

Q:

5.(20pts) Let X1, ..., Xn be a random sample from N(1, 2 1 ). Let Y1, ..., Yn be a random sample from N(2, 2 2 ). Besides, Xi is independent of Yj for all i, j. In addition, 1, 2 , 2 1 , 2 2 are...

Q:

Let y 1 , y 2 , . . . , y n be a random sample from the continuous pdf f Y (y; 1 , 2 ). Let 2 = 1/n Show that the solutions of the equations E(Y) = y and Var(Y)= 2 for 1 and 2 give the same...

Q:

Why is the solvency of insurers of such great importance to regulators?

Q:

There are four stages of the consumer decision-making process: problem recognition, information search, decision-making, and post-purchase evaluation. Please explain these four parts in about 600 -...

Q:

Fundamental value of a firm is determined by estimating: Group of answer choices Expected value of its free cash flows discounted at weighted average cost of capital Present value of its past free...

Q:

What was the main difference between the psychological thinking of Wilhelm Wundt and earlier philosophers who were also interested in thinking and behavior? a. Wundt was European, earlier...

Q:

Five cards are dealt from a standard 52-card deck. What is the probability that the sum of the faces on the five cards is 48 or more?

Q:

A somewhat inebriated conventioneer finds himself in the embarrassing predicament of being unable to predetermine whether his next step will be forward or backward. What is the probability that after...

Q:

An urn contains twenty chips, numbered 1 through 20. Two are drawn simultaneously. What is the probability that the numbers on the two chips will differ by more than 2?

Q:

The economic conditions we estimated for the next 20 years are given below 6 years super-growth (6/20=0.3) 5 years good (5/20=0.25) 5 years normal (5/20= 0.25) 4 years bad (4/20=0.20) Economy...

Q:

You are saving for the college education of your two children. They are two years apart in age; one will begin college in 6 years, and another in 8 years. You estimate your first childs college...

Q:

Answer the following in approximately 500 words total. Using the attached grading rubric. 1. Explain the fundamental differences between the traditional sales and the content marketing funnel in...