it
shoud be 0<= theta<= 3. plz type it and answe both a and b.
thank youHomework Answers
(A) moment estimation
E(X) =sum{ x*p(X=x)} = (3-thita)/3
=>4/10 =1-(thita/3)
=> thita/3 = 0.6
=> thita^ =1.8 answer
(B) MLE
Likelihood ={p( X=0)*p(X=1)}
=( thita/3)*(3-thita)/3 =(3*thita-thita^2)/9
Differentiate w.r.t thita and equate to zero
thita ^=3/2= 1.5
Add Answer to:
it
shoud be 0<= theta<= 3. plz type it and answe both a and b.
thank...
(1 point) A random variable with probability density function p(x; 0) = 0x0–1 for 0 <x<...
(1 point) A random variable with probability density function p(x; 0) = 0x0–1 for 0 <x< 1 with unknown parameter 0 > 0 is sampled three times, yielding the values 0.64,0.65,0.54. Find each of the following. (Write theta for 0.) (a) The likelihood function L(0) = d (b) The derivative of the log-likelihood function [ln L(O)] = dᎾ (c) The maximum likelihood estimate for O is is Ô =
2. Suppose Xi,X2,..., Xn are i.i.d. random variables such that a e [0, 1] and has...
2. Suppose Xi,X2,..., Xn are i.i.d. random variables such that a e [0, 1] and has the following density function: r (2a) (1a-1 where ? > 0 is the parameter for the distribution. It is known that E(X) = 2 Compute the method of moments estimator for a
Can you explain how to do parts a-c? 4. Suppose that X is a discrete random...
Can you explain how to do parts a-c?
4. Suppose that X is a discrete random variable with 2 P(X 0) Chapter 8 Estimation of Parameters and Fitting of Probability Distributions P(X = 1) = ) 2 P(X = 3) =-(1-9) where 0 θ 1 is a parameter. The following 10 independent observati were taken from such a distribution: (3, 0, 2, 1, 3, 2, 1, 0, 2, 1). a. Find the method of moments estimate of e. b. Find...
The Pareto probability distribution has many applications in economics, biology, and physics. Let β> 0 and...
The Pareto probability distribution has many applications in economics, biology, and physics. Let β> 0 and δ> 0 be the population parameters, and let XI, X2, , Xn be a random sample from the distribution with probability density function zero otherwise. Suppose B is known Recall: a method of moments estimator of δ is δ = the maximum likelihood estimator of δ is δ In In X-in β has an Exponential (0--) distribution Suppose S is known Recall Fx(x) =...
2. A discrete random variable X has the following pmf A random sample of size n...
2. A discrete random variable X has the following pmf A random sample of size n 30 produced the following observations: (a)) Find and s for this sample Find E(X) and var(X) (iii) Find the method of moments estimate of θ (iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the maximum likelihood estimate of θ is -1 fo/n, where fo is the number of observed 0's in the sample. (iii) Find...
4.8. Let Z be a random variable with the geometric probability mass function where 0 <...
4.8. Let Z be a random variable with the geometric probability mass function where 0 < π < 1. (a) Show that Z has a constant failure rate in the sense that PriZ kZk1 T for k 0, 1,.... (b) Suppose Z' is a discrete random variable whose possible values are 0, 1, and for which Pr(Z'=KZ2k} = 1-π for k 0,1,.... Show that the probability mass function for Z' is p(k).
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; =...
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; = 1) = 01, P(Y; = 2) = 62, where the parameter vector 6 = (60,61,62) satisfies: 0; > 0 and 200; = 1. (a) Calculate E[Y] and EY?), and use the results to derive a method of moments estimator for the parameters (01,02). (b) Show that the maximum likelihood estimator for 6 = 60, 61, 62) is - Ôno = ôz = = 1(Y;=0),...
2) Let X and Y be independent exponential random variables with means E[X] = 0 and...
2) Let X and Y be independent exponential random variables with means E[X] = 0 and EY = 28. 1 1 f(310) = -X/0 e x > 0, f(y|0) = e-4/20 y > 0 0 24 a) Show that the likelihood function can be written as (2 points) L(0) = e-3(x+3) 202 b) Find the MLE ô of 0. (5 points)
FF1:18 1H20B B 80 ma2500a16-1 ma2500s14 ma2500a15 ma2500s15 ma2500a17 2. Let Xi, X2 , X10 be...
FF1:18 1H20B B 80 ma2500a16-1 ma2500s14 ma2500a15 ma2500s15 ma2500a17 2. Let Xi, X2 , X10 be a random sample of observations from the N(μ, σ*) distribution where μ is unknown and σ2-10. We reject the null hypothesis Ho : μ-5 in lavour of the alternative hypothesis H1 : μ < 5 if sum of the observations is less than or equal to 35 (a) What is the critical region for the test? (b) Compute the size of the test (c)...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
(1 point) A random variable with probability density function p(x; 0) = 0x0–1 for 0 <x< 1 with unknown parameter 0 > 0 is sampled three times, yielding the values 0.64,0.65,0.54. Find each of the following. (Write theta for 0.) (a) The likelihood function L(0) = d (b) The derivative of the log-likelihood function [ln L(O)] = dᎾ (c) The maximum likelihood estimate for O is is Ô =
2. Suppose Xi,X2,..., Xn are i.i.d. random variables such that a e [0, 1] and has the following density function: r (2a) (1a-1 where ? > 0 is the parameter for the distribution. It is known that E(X) = 2 Compute the method of moments estimator for a
Can you explain how to do parts a-c?
4. Suppose that X is a discrete random variable with 2 P(X 0) Chapter 8 Estimation of Parameters and Fitting of Probability Distributions P(X = 1) = ) 2 P(X = 3) =-(1-9) where 0 θ 1 is a parameter. The following 10 independent observati were taken from such a distribution: (3, 0, 2, 1, 3, 2, 1, 0, 2, 1). a. Find the method of moments estimate of e. b. Find...
The Pareto probability distribution has many applications in economics, biology, and physics. Let β> 0 and δ> 0 be the population parameters, and let XI, X2, , Xn be a random sample from the distribution with probability density function zero otherwise. Suppose B is known Recall: a method of moments estimator of δ is δ = the maximum likelihood estimator of δ is δ In In X-in β has an Exponential (0--) distribution Suppose S is known Recall Fx(x) =...
2. A discrete random variable X has the following pmf A random sample of size n 30 produced the following observations: (a)) Find and s for this sample Find E(X) and var(X) (iii) Find the method of moments estimate of θ (iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the maximum likelihood estimate of θ is -1 fo/n, where fo is the number of observed 0's in the sample. (iii) Find...
4.8. Let Z be a random variable with the geometric probability mass function where 0 < π < 1. (a) Show that Z has a constant failure rate in the sense that PriZ kZk1 T for k 0, 1,.... (b) Suppose Z' is a discrete random variable whose possible values are 0, 1, and for which Pr(Z'=KZ2k} = 1-π for k 0,1,.... Show that the probability mass function for Z' is p(k).
2. Suppose Y1,...,Yn are IID discrete random variables with P(Y; = 0) = 60 P(Y; = 1) = 01, P(Y; = 2) = 62, where the parameter vector 6 = (60,61,62) satisfies: 0; > 0 and 200; = 1. (a) Calculate E[Y] and EY?), and use the results to derive a method of moments estimator for the parameters (01,02). (b) Show that the maximum likelihood estimator for 6 = 60, 61, 62) is - Ôno = ôz = = 1(Y;=0),...
2) Let X and Y be independent exponential random variables with means E[X] = 0 and EY = 28. 1 1 f(310) = -X/0 e x > 0, f(y|0) = e-4/20 y > 0 0 24 a) Show that the likelihood function can be written as (2 points) L(0) = e-3(x+3) 202 b) Find the MLE ô of 0. (5 points)
FF1:18 1H20B B 80 ma2500a16-1 ma2500s14 ma2500a15 ma2500s15 ma2500a17 2. Let Xi, X2 , X10 be a random sample of observations from the N(μ, σ*) distribution where μ is unknown and σ2-10. We reject the null hypothesis Ho : μ-5 in lavour of the alternative hypothesis H1 : μ < 5 if sum of the observations is less than or equal to 35 (a) What is the critical region for the test? (b) Compute the size of the test (c)...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
Most questions answered within 3 hours.
-
At the Pinelands University Medical Center, clinics trials were
performed with a medical treatment intended to...
asked 4 minutes ago -
Propose the importance of the financial account (from the BOP)
to economic indicators.?
asked 6 minutes ago -
Please submit the following files for this
assignment:
**************************Animal.h, Animal.cpp,
Mammal.h, Mammal.cpp, Cat.h, Cat.cpp,
main.cpp********************************************************
Assignment...
asked 7 minutes ago -
Question 1.
XOR
Challenge 1: The key is a single digit
Decrypt the cipher =
snw{fzs...
asked 10 minutes ago -
Multidimensional arrays can be stored in row major order or in
column major order. The access...
asked 9 minutes ago -
A study is conducted
to determine the simple linear regression relation (if any) between
average temperature...
asked 28 minutes ago -
Twenty percent of all telephones of a certain type are submitted
for service while under warranty....
asked 58 minutes ago -
Which is a method of transmitting pathogens from one host to
another by carrying microorganisms inside...
asked 37 minutes ago -
In a memo written to a US trade policy maker, outline an
argument for the role...
asked 29 minutes ago -
Ten young adults living in California rated the taste of a newly
developed sushi pizza topped...
asked 49 minutes ago -
In a titration experiment, 29.9 mL of 0.797 M HCOOH neutralizes
20.6 mL of Ba(OH)2. What...
asked 45 minutes ago -
A
roller coaster cart of mass 312 kg travels around a horizontal
curve of radius 41.3...
asked 59 minutes ago