The image contains a problem and a table related to joint distribution in statistics. Here’s the transcription:---3. Let \( X \) and \( Y \) have the joint distribution as indicated in the following table:\[\begin{array}{c|ccc} & Y=0 & Y=1 & Y=2 \\\hlineX=0 & 1/3 & 0 & 1/3 \\X=1 & 0 & 1/3 & 0 \\\end{array}\]a. Give \(\hat{Y}_L\), the linear MMSE (Minimum Mean Square Error) estimate for \( Y \) given \( X \).b. Give the MSE (Mean Square Error) for \(\hat{Y}_L\).c. Give \(\hat{Y}_M\), the MMSE estimate for \( Y \) given \( X \).d. Give the MSE for \(\hat{Y}_M\).---**Explanation of the Table:**The table presents the joint probability distribution of two random variables, \( X \) and \( Y \). The rows of the table represent different values of \( X \), while the columns represent different values of \( Y \). Each cell in the table shows the probability that \( X \) and \( Y \) take on the values specified by the respective row and column. - For \( X = 0 \), \( Y = 0 \) has a probability of \( \frac{1}{3} \), \( Y = 1 \) has a probability of \( 0 \), and \( Y = 2 \) has a probability of \( \frac{1}{3} \).- For \( X = 1 \), \( Y = 0 \) has a probability of \( 0 \), \( Y = 1 \) has a probability of \( \frac{1}{3} \), and \( Y = 2 \) has a probability of \( 0 \).

Answered: Image /qna-images/answer/9de852ba-b991-44a8-804c-2f47a989bc18.jpg

Answered: 3. Let X and Y have the joint…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on x = frying time (sec) and y = moisture content (%) appeared in an article. x 5 10 15 20 25 30 45 60 y 16.4 9.7 8.1 4.2 3.3 2.8 2.0 1.2 (a) Construct a scatter plot of y versus x. y 15 10- 5 y 15 O 10 10 20 30 40 50 5 10 20 10 NE X 50 60 30 60 40 X 15 y 10 O 5 O y 15 10 20 30 40 50 60 10 20 30 Comment. The plot has a curved pattern. A linear model would not be appropriate. O The plot has a curved pattern. A linear model would be appropriate. O The plot does not have a curved pattern. A linear model would be appropriate. O The plot does not have a curved pattern. A linear model would not be appropriate. 40 50 60 X X
Which of the following is the closest estimate of r for the following scatterplot? a. .4 b. 0 c. -.9. d. -.4
A drug company claims that their products’ contaminations never vary by more than 2%. Sample of 5 specimens were tested and the percentages of the purities are recorded as Observation no. 1 2 3 4 5 Percentages (%) 98.6 97.2 98.9 97.7 97.9 a. Do the sample data have enough proof to oppose the manufacturer’s claim? (HINT: take the range of 2% equal 4σ.) b. Find a 90% confidence interval for σ2.
#23).
#23). Need help solving problem.
Q2. A laundry for car wash found that the average, for small size car, cleaning time is 5 mins in the morning and 6.5 mins at evening time when a sample of size 30 is taken at the two time periods. From the previous record, the laundry manager knew that car oj = 2 mins for the morning shift and oz = 2.5 mins for morning and evening repectively. Find the interval estimate for 4 - 42 with 90% confidence level.
The model Yị = Bo + B, In X;+e; was estimated using E-Views and the results are shown in the following Table. What is the value of the slope at X = 10 Dependent variable: Y Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. 53.26667 5.770449 9.230940 0.0000 In (x) 0.929992 0.0075 -3.303030 R-squared Mean dependent var 35.10000 Adjusted R-squared.. S.D. dependent var 12.78410 S.E. of regression... Residuals sum square ..... ...... F-statistic Prob(F-statistic) 0.007491
A score S is used to predict whether a disease is present. If the score is greater than a threshold value, the corresponding person is classified as ill, otherwise as healthy. Here, the scores S; for 9 persons are given. Furthermore, it is known whether the persons are actually ill (Y, = 1) or not (Yi = 0). The data look as follows: S; | Y; 0.3 0 1.2 1 0.7 0.8 1 0.1 0.4 1 1.1 0 0.2 0 1.4 1 (a) Draw by hand the ROC curve for the given data. Explain your procedure and the calcu- lation methods. (b) Calculate the area under the curve (AUC) by hand. Does this value indicate a good or bad classification? (c) Calculate the partial area under the curve (PAUC) if the specificity is to be at least 0.65. How do you judge this value?
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal distribution?
Solve for C
Consider the following data relating hours spent studying (X) and average grade on course quizzes (Y): X Y 5 6 3 8 4 8 7 10 5 7 6 9 Compute SSX 10 30 5 44
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. i need help with (c), sketching the distribution, (d) and (e)

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

3. Let X and Y have the joint distribution as indicated in the following table: X=0 X=1 |Y=0 1/3 0 Y=1 0 1/3 Y=2 1/3 0 a. Give Y, the linear MMSE estimate for Y given X. b. Give the MSE for Ŷ₁. c. Give YM, the MMSE estimate for Y given X. d. Give the MSE for ÎM.