3. (a) Based on the random sample Y1 = 5.2, Y24.6, use themethod of maximum likelihood to estimate the parameter 0 in the uniform pdf2.8, Y311.2, Yfr (y;0)0 ys0.(b) Suppose the random sample in part (a) represents the two-parameter uniform pdf1fr (y; 01, 02)01y02.01 02Find the maximum likelihood estimates for 01 and 02.

Question
Asked Oct 30, 2019
3. (a) Based on the random sample Y1 = 5.2, Y2
4.6, use the
method of maximum likelihood to estimate the parameter 0 in the uniform pdf
2.8, Y3
11.2, Y
fr (y;0)
0 ys0.
(b) Suppose the random sample in part (a) represents the two-parameter uniform pdf
1
fr (y; 01, 02)
01y02.
01 02
Find the maximum likelihood estimates for 01 and 02.
help_outline

Image Transcriptionclose

3. (a) Based on the random sample Y1 = 5.2, Y2 4.6, use the method of maximum likelihood to estimate the parameter 0 in the uniform pdf 2.8, Y3 11.2, Y fr (y;0) 0 ys0. (b) Suppose the random sample in part (a) represents the two-parameter uniform pdf 1 fr (y; 01, 02) 01y02. 01 02 Find the maximum likelihood estimates for 01 and 02.

fullscreen
check_circleExpert Solution
Step 1

Note:

The pdf in Part (b) will be fY (y; θ1, θ2) = 1/(θ2 θ1) if θ1y θ. We have solved using this pdf.

Step 2

Introduction:

The maximum likelihood estimator (MLE) of a parameter θ is an estimator that maximizes the likelihood or probability of the set of observed data.

Step 3

Part (a):

The MLE for θ is Y3 = 11.2 calculated below:

...
Likelihood function
L(y)- II(y0)
-1
Log-likelihood function:
(y)-In[L(y)]
-nln
Differentiating with respect to 0
S(y)
increasing fiunction of 0, maximum for Y
ө
max
se
max
11.2
MLE is e11.2.
help_outline

Image Transcriptionclose

Likelihood function L(y)- II(y0) -1 Log-likelihood function: (y)-In[L(y)] -nln Differentiating with respect to 0 S(y) increasing fiunction of 0, maximum for Y ө max se max 11.2 MLE is e11.2.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Bill commutes to work in the business district of Boston. He takes the train 2/5 of the time and dri...

A: Let Y be the takes the train, D be he takes the train, and A be the drives the time.Therefore, it is...

question_answer

Q: A certain flight arrives on time 82 percent of the time. Suppose 198flights are randomly selected. U...

A: It is given that 82% of the time the flight arrives on time. Therefore, probability of a selected fl...

question_answer

Q: After conducting a re-test for independent samples, you arrived at the following:t(47) = 3.41, p<...

A: Given information:From the given information the following information can be observed:The test stat...

question_answer

Q: In your own words, compare and contrast the general steps involved in computing the F-ratio between ...

A: Repeated measures ANOVA is equivalent to one-way ANOVA but it for related group. Repeated measure AN...

question_answer

Q: 6. Suppose a researcher used data on a group of third year students at MIT to estimate the following...

A: Given dataLine of best fitterm GPA=0.625+0.024atndrte1)If the sample mean atndrte is 82, sample mean...

question_answer

Q: A clinical trial tests a method designed to increase the probability of conceiving a girl. In the st...

A: Given datan = 600x = 330Sample proportion is given by

question_answer

Q: Find the mean of the data summarized in the given frequency distribution. 12) The highway speeds of ...

A: Mean for grouped data:The formula to find mean for grouped data is as follows:

question_answer

Q: The US population is 13% African American.  If you were to take a SRS of 500 Americans, above what p...

A: Solution:From the given information, the proportion of African American is 0.13, random sample of si...

question_answer

Q: Calculate the variance and standard deviation  449,489,548,579,337,424,567,472,392,291,527,449,460,6...

A: Given,449,489,548,579,337,424,567,472,392,291,527,449,460,622Standard deviation is a measure of disp...