• Exercise 2Let Y be a random variables with density functionfy (y) =aya-1for y E (0,0)where 6> 0 and a > 0.You know that a = 2 and you want to estimate 0. Show that the samplemean Y is a biased estimator for 0, and find a constant k such that kY isa unbiased estimator for 0.!3!

An estimator Ty is said to be an unbiased estimator for θ ifE(Ty)=θ ∀θ∈Θ

• Exercise 2 Let Y be a random variables with density function fy (y) = aya-1 for y E (0,0) %3D where 0 > 0 and a > 0. You know that a = mean Y is a biased estimator for 0, and find a constant k such that kY is a unbiased estimator for 0. 2 and you want to estimate 0. Show that the sample

• Exercise 2 Let Y be a random variables with density function fy (y) = aya-1 for y E (0,0) %3D where 0 > 0 and a > 0. You know that a = mean Y is a biased estimator for 0, and find a constant k such that kY is a unbiased estimator for 0. 2 and you want to estimate 0. Show that the sample

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: The joint distribution for the length of life of two different types of components operating in a…

A: Thanks for giving opportunity to serve for bartleby students, Hey, There ! Thank you for posting…

Q: X is a random variable whose density function is f(X) = A e*, 0<x<c∞ = 0 otherwise Find the value of…

A: As per the policies, only 3 subparts can be solved, to get the other questions solved, kindly repost…

Q: Consider the random variables X and Y with joint density function. 0 0.5, Y > 0.5).

A: Given,f(x,y)=x+y; 0≤x,y≤10; elsewhere

Q: Let X be a random variable from an exponential distribution with parameter 1/2. Calculate the…

Q: Let X1, X2,...,Xn be a random sample of size n from a distribution with probability density function…

A: Introduction: In order to find the maximum likelihood estimator (MLE) of α, first differentiate the…

Q: Let X be the random variable with the density function f(x) given by 2.2 3.2 if a >0 f(x) = (1+z)3…

Q: A random variable Y is said to have a Singh-Maddala distribution with parameter θ > 0 if the density…

Q: Let Y, Y2, ., Yn denote a random sample from N(0,0) distribution with probability density function:…

Q: Two electronic components of a missile system work in harmony for the success of the total system.…

Q: a. Is Y discrete or continuous? Explain. Plot the PMF/PDF of random variable Y (whichever is…

A: For the given data a. Is Y discrete or continuous? Explain. Plot the PMF/PDF of random variable Y…

Q: A random sampleY1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density function is…

A: From the given information, the probability density function is, f(y)=βe-βy, y>0, β>0.…

Q: y > 0, A random variable Y has density f(y) = ey TY else. Identify this distribution by name and the…

A: Given: fy=1eyπy, y>00, otherwise

Q: for y > 0 where 0 > 0 is a parameter. Determine the rejection region for the significant level a…

Q: 3y? exp 03 f(y|0) y > 0, 03 here 0 > 0 is a parameter. Using an appropriate pivotal quantity, verify…

Q: ELT(Let) the joint probabilty density function of two con random variable Y and X Find P(Y>=X)…

Q: A continuous random variables X has the density function 1 f(x) = ,x> 0 Otherwise Find the expected…

Q: b) Let Y, Y, .,Y, be a random sample from a population with probability density function in part a).…

Q: Let X be a continuous random variable with the density fy (x) = e-* for x> 0 and let Y= e 7X/ 10 The…

A: Given,f(x)=e-x ; x>0and Y=e7x10

Q: ELT(Let) the joint probabilty density function of two con random variable Y and X. Please do the…

Q: Let X1, X2, ..., Xn be a random sample of size n from a distribution with probability density…

Q: A continuous random variable X has the density function given f(x)= A.e 6. Find the value of A and…

Q: B1. Let us consider a random variable X following a Weibull distribution with parameter k = 2 and A…

A: Given the following random numbers sampled from the uniform distribution on the interval [0,1],u1…

Q: The length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport…

Q: A civil engineer is studying the live loads on a highway bridge. Let Y and Z denote the live load…

Q: Let X1, X2,...,X, be a random sample of size n from a distribution with probability density function…

Q: Q. 6 The percentage of impurities per batch in a chemical product is a random variable X with…

Q: ] The joint density function of two continuous random variables X and Y is: Scx²e-y/3 1<x < 6, 2 <…

A: a) From the given information, the joint density function of two continuous random variables X and Y…

Q: Suppose X and Y are random variables with joint density function. Rx, y) = { 0.1e-(0.5x + 0.2y) if…

A: see the solution

Q: The error in the length of a part, in mm, is a random variable X with probability density function…

A: a.) The mean error is given by…

Q: Let X1,..., Xn be iid random variables with the density function f(x;0) = (0+ 1)xº for 0 <x < 1. (a)…

A: Let X1,X2,...Xn be iid random variables with pdf given by, f(x,θ)=(θ+1)xθ ; for 0≤x≤1

Q: The common probability density function of the random variables X, Y is given below. z+ cy? 0<I<1,0<…

A: We have given that, The common probability density function of the random variables X, Y is given…

Q: Let X1,· ·. Xn be iid random variables with the density function f(x; 0) = (0+1)x° for 0 < x<1. a)…

A: Statistic is a function of sample observation. A statistic is said to be a sufficient statistic if…

Q: Calculate the 30th percentiles of X. (Round to 2 decimals).

A: The density function is, fx=2.52002.5x3.5 for x≥2000 otherwise The…

Q: Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 <…

Q: Answer part a of the following question. Show work. Let Y > 0 be a continuous random variable…

A: From the given information, the random variable Y>0 be a continuous random variable representing…

Q: () Briefly explain how moment generating function of a random variable, y may be used to Generate…

A: As per bartleby guideline if more than one question asked only first question to be answered kindly…

Q: A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is…

A: Given f(y) = ay0αyα+1 if y > y00 , elsewhere

Q: a) Verify that [4xy if 0 <x < I, 0 < y< 1 f(x, y) = otherwise is a joint density function. b) If X…

Q: The random variables X,, X2,..., Xn are independent and identically distributed random vari- ables…

Q: A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is…

A: Solution

Q: A random variable Y has the density function e", y< 0 f(y) = { 0 otherwise Find E(Y³). Please round…

Q: Suppose X and Y are random variables with joint density function. f(x, y) = 0.1e−(0.5x + 0.2y)…

Q: A continuous random variable X has density function f(x) = 1.5(1 – x²), 0 < x < 1. a) Calculate the…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: ) Let Y1, Y2, ..., Yn be a random sample from a population with probability density function in part…

Q: The total number of hours, measured in units of 100 hours, that a family uses a vacuum cleaner in a…

A: Given that ; A continues random variable x ... And a pdf is given. Wi5h help of this per and by…

Q: A student tossed a fair coin three times. She decided to let X to be a random variable that takes…

A: Solution: As per the guidelines only first three sub-parts should be answered. In case remaining…

Q: A random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is…

A: Solution

Q: The joint pdf of a bivariate random variable (X,Y) is given by [Kx²y, x₁ = 1,2; y, = 1,2,3 Px,y (x₁,…

A: From the given data: P(xi,yi)=kxi2yi xi=1,20…

Q: (a) Let X and Y be random variable with the joint density function. fxy (x, y) = 2 for 0 <x <y< I…

Q: EXCERSISE Suppose X. X,, ...X, are i.i.d. random variables with density function f(x|0) = , exp (-),…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

• Exercise 2
Let Y be a random variables with density function
fy (y) =
aya-1
for y E (0,0)
where 6> 0 and a > 0.
You know that a = 2 and you want to estimate 0. Show that the sample
mean Y is a biased estimator for 0, and find a constant k such that kY is
a unbiased estimator for 0.
!3!

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

A random variable Y is said to have a Singh-Maddala distribution with parameter θ > 0 if the density function of Y isf(y|θ) = 2θy(1 + y2)θ+1for y > 0. Suppose that Y1,Y2,...,Yn is a random sample from a Singh-Maddala(θ) population where θ > 0 is a parameter.(a) Verify that f(y|θ) belongs to an exponential family in traditional form.(b) Compute the likelihood function L(θ) for this random sample.(c) Determine θˆMLE, the maximum likelihood estimator of θ. You may use any method that we discussed in class for finding the MLE.(d) Find the Fisher information I(θ) in a single observation from this density.(e) Using the standard normal approximation for the distribution of a maximum likelihood es- timator based on the Fisher information, construct an approximate 95% confidence interval for θ. Note that z0.025 = 1.96.Note that the Singh-Maddala distribution is also known as the Burr Type XII distribution and is used in economics and actuarial science to model income sizes.
Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.
Let (X,Y) be a two-dimensional random variable with the density function below. So P(X>1/2 | Y>1)=P(X>1/2)? **continuation on image** **caso contrário = otherwise**
X is a uniform random variable over the interval (3, 5). Find the density function of X for the interval (3, 5)
Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise Find the constant c, Find the marginal distribution functions(cdfs) for X and Y, Find the marginal density functions(pdfs) for X and Y, P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),
b) Let Y1, Y2, ..., Yn be a random sample from a population with probability density function in part a). Show that the best test for the hypothesis in part a) rejects Ho if |yi <c i=1 where c solves the probability equation a = P(II1Yis c[0 = 2). c) Let X1,X2, ..., Xn be a random sample from GAMMA(2,ß) distribution, and consider Y = E-,Xi- Show whether or not Y is a pivotal quantity and give its distribution.
1)Let x and y be two continuous random variables whose function is the probability density joint is given by : a)Draw the relationship between the variables x and y on the Cartesian axes .b)Calculate the marginal pdfs px(X)and py(Y).c)Are the v.a.s x and y independent ?
The joint probability mass function of the two random variables (X, Y) is given by f(x,y) = { 1/5(3x-y), 1<=x<=2 , 1<=y<=3 0 , otherwise• Find the P( X ≤ Y)• Find the marginal density functions of X and Y• Are X and Y independent?• Find E(XY)
The combined density function fxy(x, y) formed by continuous X and Y random variables is given below. According to this; Calculate the options a, b, c, d, e, f, g, h, i .
ELT(Let) the joint probabilty density function of two con random variable Y and X. Please do the last three sigma x, y and PXY
Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.
The number of minutes that train is early or late can be modeled by a random variable whose density is given by: g(t) = {(1/972)(81 − t^2), −9 ≤ t ≤ 9, 0 elsewhere, where negative values indicate the train arriving early and positive values indicate the train arriving late. a. Find the probability that one of the train trips will arrive more than 5 minutes early. b. Find the probability that one of the train trips will arrive between 1 and 8 minutes late. c. Without integration, give the expected number of minutes early/late. Examination of the graph and recollection of properties of integrals will allow this.