Problem 8Suppose that X1, X2,X10 are iid exponential random variables.a. What is the joint density of X1,X 10 at x1, ... , .· , X10?b. Show that the likelihood ratio test for the null hypothesis 1 = 1.1 versus the alternate 1 = 2.1 with a = 0.05can be written in the form: reject Ho when S < C for some constant C, where S = X1 + ·… + X10-c. Find C that makes a = 0.05.d. What is ß for your test?

Disclaimer: As question has multiple parts, only first three will be answered. X1, X2, ..., Xn are…

Suppose that X1, X2, .. , X10 are iid exponential random variables. a. What is the joint density of X1,. X10 at x1, ... , X10? ... b. Show that the likelihood ratio test for the null hypothesis 2 = 1.1 versus the alternate å = 2.1 with a = 0.05 can be written in the form: reject Ho when S

Suppose that X1, X2, .. , X10 are iid exponential random variables. a. What is the joint density of X1,. X10 at x1, ... , X10? ... b. Show that the likelihood ratio test for the null hypothesis 2 = 1.1 versus the alternate å = 2.1 with a = 0.05 can be written in the form: reject Ho when S

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: 2. Suppose that Y; ~ N(Bxi,o²) for i = 1, 2, ..., n, all independent, where x; is a known covariate.…

A: Given that Yi~Nβxi, σ2 for i=1, 2, ...,n, all independent, where xi is a known covariate.

Q: Consider a discrete random variable X with a pmf given by i) ii) iv) p(x) = cx2, if x = 1,2,3,4 0,…

Q: iid Normal (0, 1). In each of the following cases, identify the distribution of the Let X1, X2, X3…

A: Note: Since you have posted a question with multiple subparts, we will solve the first three…

Q: Problem 2. Let X1,..., X, be any n random variables such that |Cov(X;, X;)| < 0, i, j 1,..., n. Let…

Q: 10. , Let X(1 ≤ k ≤ n) be independent random variables and B~ Bernoulli(pk)(1 ≤ k ≤ n) be…

A: In this problem, we are given independent random variables and Bernoulli random variables . The…

Q: The number of failures of a testing instrument from contamination particles on the product is a…

A: GivenMean of failure per hour is 0.02λ=0.02Let x be the no.of failure per…

Q: The members of University of cape Town Volleyball group are selling branded UCT caps from room to…

A: The sample size is .The probability that the group will sell at least one cap in any room is .

Q: Suppose that Z is a discrete random variable with Var(Z) = 1/2 a quantities. %3D Var(2 – Z) Drag…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: 2. Let X and Y be independent random variables with means µx and μy and variances of and o,…

A: Given that Two variables X and Y are independent random variables. EX=μXEY=μYVarX=σXVarY=σY The…

Q: An extreme Type Il random variable X has parameters u = 6.9 andk= 4.9. What is the probability that…

A: Given that a random variable X follows an extreme Type II distribution with parameters u=6.9 and…

Q: voters who either voted for Candidate A ("X, = l") or for Candidate B ("X; = 0"). Denote the…

A: A random sample of x1,x2,...xn voters were there voting for 2 candidates A and B Hypothesis : The…

Q: The random variables X₁, X₂ have the same distribution as shown follows Xi P 0 1/2 1 1/4 2 1/4 Where…

A: Here, we are given that the random variable X1, X2 have the same distribution…

Q: In a certain country, the amount of annual rainfall (in tonnes per m) is modelled through a Gamma…

A: Given that the random variable X as the Gamma distribution with α=2 and λ=3. The probability density…

Q: A special discrete whole life insurance is issued to (80). The death benefit is 1000 if death occurs…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let X1, X2,..., Xn ~ N(μ, 0²) independent random variables. Find the distribution X+X2+…+Xn X= = n…

A: Given Xi~N(μ, σ2) be the iid and i=1,2,...,n Result: X and Y are independent then E(XY)=E(X)E(Y)…

Q: Suppose that Y is a discrete random variable with mean u and variance o and let W = 5Y. (a) Do you…

Q: B. Let y1, y2, ..., Yn be a random sample from N(µ, o) distribution, where of is known. We wish to…

A: Solution:

Q: Suppose I flip n independent biased coins such that the jth coin has probability j/n of being heads,…

A: n independent biased coins are collected. Define the random variables, Xj = 1if j th coin results…

Q: Let X1 and X2 be two independent and identically distributed random variables with N(µ, 1)…

A: Given:: Let X1 and X2 be two independent and identically distributed random variables with N(µ, 1)…

Q: Let X1, X2, ..., Xn be a random sample from U(0,0) distribution. Find the most powerful test of Ho :…

Q: Let X1, X2, ...X, be an i.i.d. N(1, 202) sample. (1). Write down the likelihood function for the…

Q: Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. [a] How can…

A: We have given thatVar[X] = 4.8Var[Y] = 9.7X and Y are independent random variables.That is,…

Q: i.i.d. 4. (Pooled z-test as likelihood ratio test) Let X1,..., Xm N(1, 1) and Y₁,..., Yn Suppose…

A: If you have any queries, please comment.

Q: 2. Let X₁,..., Xn be a random sample from a Bernoulli (0) distribution, where 0 < 0 < 1. (a) Show…

Q: Let X₁, X₂ be independent random variables with mean and variance o, and a is a constant. We also…

A: Given that X1,X2 be independent random variables with mean μ adn variance σ2. So, E(X1)=μ=E(X2) and…

Q: Let X and Y have a bivaraite gamma distribution of Kibble with parameters a = 1 and 0<0< 1. What is…

Q: Let x be a continuous random variable that has a normal distribution with a mean of 50 and a…

Q: If X1,X2,...,Xn constitute a random sample of size n from a gamma population with α =2, use the…

A: Xi ~ gamma(ɑ=2 , β) ; i=1,2,...,n

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor Therefore, X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: Example 5.4 Consider a random sample (X1. X2..X) from an exponential dis- tribution with parameter…

Q: Suppose that the random variables Y1, . , Yn satisfy Y, = B ; + e, i= 1,..., n, where #1, ..., In…

A: From the given information, Y1, Y2,....,Yn satisfy Yi=βxi+εi, i=1,2,....,n. Here, x1,x2,....,xn are…

Q: i.i.d. 4. (Pooled z-test as likelihood ratio test) Let X1,..., Xm N(μ1, 1) and Y₁,..., Yn Suppose…

A: Step 1: Step 2:

Q: Suppose that X is a discrete random variable, and suppose that the probability mass function of X is…

A: Given that Probability distribution table. X 0 10 20 30 P(x) 0.4 0.3 0.2 0.1 NOTE:-…

Q: Let X1, . . . , Xm i.i.d.∼ N (μ1, 1) and Y1, . . . , Yn i.i.d.∼ N (μ2, 1).Suppose that these two…

A: Step 1:Step 2:Step 3:

Q: Let the random variable X denote the number of trials in ecess of r that are ed to achieve the r-th…

A: Given that, The random variable X as the number of trails in excess of r that are required to…

Q: Exercise 13. Let X₁,..., Xn~ N(x, o2) i.i.d. and Y1₁,..., Yn~ N(My, 02) i.i.d. with known o². We…

A: Let X1,X2,...,Xn~Nμx,σ2 iid and Y1,Y2,...,Yn~Nμy,σ2 iid with known σ2. Di=Xi-Yi EDi=μx-μy VarDi=2σ2…

Q: A transmitter sends out a random number X which can take values of -1, 0, or 1, each with…

A: X can take the values of -1, 0, or 1, each with probability 13. So, the PMF of X is P(X=x)=13,…

Q: 4. Determine the values of c so that the following functions represent joint probability…

A: The question is about joint probability distribution.Given :

Q: 3. Suppose X1 and X2 are independent random variables w. Let U = X1 and V = X1+X2. Find p(U, V) in…

A: Result X1 and X2 are independent, then Cov(X1, X2)=0

Q: Suppose that Y₁, Y₂, ..., Y₁ is a random sample from a normal distribution with parameter mean 0 and…

Q: (6) p.d.f. X and Y are two independent continuous random variables. X and Y share the same f(t) = 3…

A: Given that X and Y are two independent random variables having the same pdf,The distribution…

Q: A hypothesis test is conducted with H0:μ=46 and H1:μ≠46. A simple random sample of size n=68 is…

A: Given information- Sample size, n = 68 Sample mean, x-bar = 52 Sample standard deviation (s) = 15…

Q: 2. Let X1, X2, ..., X, be iid random variables with a common pdf/pf f(x, 0) depending on an unknown…

A: Please see the handwritten solution.

Q: Let X1, X2,...,X3 denote a random sample from a population having mean u and variance o2. 302 Which…

Q: ) Let Yi, Ya, ...Y, be a random sample size n from a Negative Binomial distribution with parameters…

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

Problem 8
Suppose that X1, X2,
X10 are iid exponential random variables.
a. What is the joint density of X1,
X 10 at x1, ... , .
· , X10?
b. Show that the likelihood ratio test for the null hypothesis 1 = 1.1 versus the alternate 1 = 2.1 with a = 0.05
can be written in the form: reject Ho when S < C for some constant C, where S = X1 + ·… + X10-
c. Find C that makes a = 0.05.
d. What is ß for your test?

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 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

The distribution of the binomial random variable (X) has the following parametes: P=0,3 and n=9. Determine P(X>2) OA. 0.9160 OB. 0,1960 OC. 0,1715 OD. 1
Suppose that Y₁, Y₂, ..., Ym is a random sample of size m from Gamma (a = 3, B = 0), where 0 is not known. Check whether or not the maximum likelihood estimator Ô is a minimum variance unbiased estimator of the parameter 8.
Consider a random variable X taking the values k1, k2, , km E R .. with probability ; Pn E [0, 1] 1. Write down the formula for the P1, P2, .. respectively, where p1 + P2 + expected value of f(X) for a given function f(-). + Pn ...
We have the following information about the random variables X and Y: |x = 1, |y = −1.5 , ox = 0.25, c} = 1. o Calculate the variance of Z = 3X + 5Y, a) when the coefficient of correlation is p(X, Y) = 0.46: 0²77 34.15 Z b) when X and Y are independent random variables: 0²2 27.75 X
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
Let (X1, X2, ..., X,) be a random sample from normal distribution i.e., N (0, 0), where the variance 0 is unknown. Consider the hypothesis test of the null hypothesis Ho : 0 = 0, where O, is the fixed positive number, against the alternative composite hypothesis H 0 > 00. Find the uniformly most powerful test of size a.
Let Y1,..., Y, be i.i.d. random variables from the Weibull distribution f(y; 0) Σ (멤) exp ), y > 0. Show that ô = Li=1í is an unbiased estimator of 0. Is Ô an efficient estimaotr of 0?
Let X be a normal random variable with = 9 and o 1.85 and Y be a normal random variable with u = 3 and o 0.45. Assume X and Y are independent. Find the following probabilities: (a) P(X 8, Y 3.75) (d) P(X < 12, 2.1 ≤Y ≤ 3.8)
Let Y1, Y2, Y3 denote independent exponential random variables with respective rates A; for i e {1,2, 3}. Answer the following questions; (a) Compute E[Y1 +Y2 +Y3]Y1 > 1, Y2 > 2, Y3 > 3]. Your answer should be an expression using A;'s. (b) Compute the probability that Yı is the smallest among three random variables. Hint: P(X < Y) = S" Px,y (x, y)dædy where Px,Y (x, y) is the joint density function.
A toll road charges $ 4 for passenger cars and $ 7 for othervehicles. LetX1be the number of passenger cars and X2 be the number ofother vehicles entering the toll road in one hour. Assume thatX1andX2are independent normal random variables with means μ1= 45, μ2= 20, andstandard deviations σ1= 5, σ2= 6. a) Express the toll road revenue per hourY as a function of X1 and X2. b) Find the mean μY and the standard deviation σY of Y. c) Find the probability that the toll road revenue during a particular hour is between $300 and $400 inclusive.
, If continuous random variable X is normally distributed with u = 5625 and o = 875.5, what is P(5000 s X s 6000)?