Exercise 1: Probability Distribution
![Exercice 1 Consider a random variable X with the following probabilities distribution: where α1 and α2 are parameters such that 0 < αι < 1,0 < α2 1 and α1taz 1. 1) Compute E[X] and E[X2]. 2) Find a. and az, two estimators of«, and α2, using the Method of Moments. 3)we assume that 22-1-12,xf 7t 6, t=1 is unbiased?](http://img.homeworklib.com/questions/e938ba00-3256-11eb-ac11-7122781e91ae.png?x-oss-process=image/resize,w_560)
Please give detailed steps for questions 2 & 3, I have seen the explanation before but it remains unclear.
Homework Answers
Add Answer to:
Exercise 1: Probability Distribution
Please give detailed steps for questions 2 & 3, I have seen...
Exercice 1: Consider a random variable X with the following probabilities distribution: 2 where α1 and...
Exercice 1: Consider a random variable X with the following probabilities distribution: 2 where α1 and α2 are parameters such that 0 < αι < 1,0 < α2 < 1 and αί+a2 1. 1) Compute E[X] and E[X21. 2) Find aǐ and , two estimators of α1 and α2, using the Method of Moments. 3) We assume that: 7t 7 1 1-1 i=1 is as unbiased?
Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
Having troubles with question 2. Please help 2. If X has a Gamma distribution with parameters...
Having troubles with question 2. Please help
2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...
Please give detailed steps. Thank you. 5. Let {X, : i-1..n^ denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
Please give detailed steps. Thank you. 2. Consider the following joint distribution of two discrete variables...
Please give detailed steps. Thank you.
2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
1. This question is on probability a. Suppose that X is a normally distributed random variable,...
1. This question is on probability a. Suppose that X is a normally distributed random variable, where X N (M, o). Show that E [cºX f (x)] = cºu+20oʻE [ f (x + 002)] where f is a suitable function and 0 € R is a scalar. Hint: Write X = 1 +o0; 0~ N (0,1) and calculate the resulting integral b. Consider the probability density function X>0 p(x) = { Az exp (-1.2-2) 10 x < 0 (>0) is...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the inte...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning. I have no...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning.
I have no clue how to do these. I know the image quality is iffy
but please help as best you can
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will...
2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x)...
2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x) = or-(-) where x 2 1 and a > 1 You may use the fact: E[X] - - 2.4 Show that the fisher information in the whole sample is: In(a)= 2.5 What Cramer Rao lower bound for unbiased estimators of a? 2.7 Consider estimating the unknown quantity: g(a) = 0 - 4+.. Determine the MLE of gla). What property are you using to justify...
Exercice 1: Consider a random variable X with the following probabilities distribution: 2 where α1 and α2 are parameters such that 0 < αι < 1,0 < α2 < 1 and αί+a2 1. 1) Compute E[X] and E[X21. 2) Find aǐ and , two estimators of α1 and α2, using the Method of Moments. 3) We assume that: 7t 7 1 1-1 i=1 is as unbiased?
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
Having troubles with question 2. Please help
2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
Please give detailed steps. Thank you.
2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
1. This question is on probability a. Suppose that X is a normally distributed random variable, where X N (M, o). Show that E [cºX f (x)] = cºu+20oʻE [ f (x + 002)] where f is a suitable function and 0 € R is a scalar. Hint: Write X = 1 +o0; 0~ N (0,1) and calculate the resulting integral b. Consider the probability density function X>0 p(x) = { Az exp (-1.2-2) 10 x < 0 (>0) is...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning.
I have no clue how to do these. I know the image quality is iffy
but please help as best you can
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will...
2 Let X1, X2, ..., X, be independent continuous random variables from the following distribution: f(x) = or-(-) where x 2 1 and a > 1 You may use the fact: E[X] - - 2.4 Show that the fisher information in the whole sample is: In(a)= 2.5 What Cramer Rao lower bound for unbiased estimators of a? 2.7 Consider estimating the unknown quantity: g(a) = 0 - 4+.. Determine the MLE of gla). What property are you using to justify...
Most questions answered within 3 hours.
-
1- What is the energy of a photon with a frequency of 7.01 ×
10¹⁴ s⁻¹?...
asked 53 seconds from now -
Illustrate the Substitution Effect, Income Effect and Total
Effect of a normal good and an inferior...
asked 49 seconds ago -
Cesar needs to make a decision whether to fertilize his garden
or not. His profit depends...
asked 1 minute ago -
Your company has six-sigma conformance for each of 10 component
that are a part if a...
asked 14 minutes ago -
Explain the buffering components of urine, the chemical
equation, where the system is found and find...
asked 20 minutes ago -
The financial records of Leon Paul Inc. were destroyed by fire
at the end of 2017....
asked 21 minutes ago -
The normal-curve approximation can also be used for discrete
distribution other than the binomial distribution. For...
asked 52 minutes ago -
1. Find the following z values for the standard normal
variable Z. (You may find it...
asked 48 minutes ago -
Lakeside Motors will sell you a $9000 car for $225 a month for 60
months. What...
asked 38 minutes ago -
how immigrants foster innovations and how it lead to economic
growth of the host country????
"Not...
asked 49 minutes ago -
What are some of the methods that creditors use to
reduce risk in credit transactions?
asked 44 minutes ago -
1 Explain HOW you would use the scientific method to test
which helps kids lose weight:...
asked 51 minutes ago