1. [25 pts] Here is a plate model.AObiect1BEFObject2a. What probability distributions do we need to specify for this model?b. Draw an unrolled version of the Bayesian network, where there are three itemsof type Object1 and two items of Object2 type.

The objective of the question is to identify the probability distributions required for a given…

Answered: 1. [25 pts] Here is a plate model. A…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A local beer company wants to produce a new Double IPA to feature in their regular rotation. Three recipes are created, each one the same but varying in terms of the type of finishing hop used for aroma: Citra, Mosaic, or Nelson Sauvin. In order to avoid carry-over effects, willing customers are randomly assigned to receive a six ounce pour of only one of the three beers. What is the best statistical test to conduct? O one sample t test O correlated groups t test O One Way Between Subjects ANOVA O One Way Repeated Measures ANOVA
A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
The table below gives the two-way classification of 400 randomly selected persons based on their status as a smoker or a nonsmoker and on the number of visits they made to their physicians last year. Suppose you must test the hypothesis at 5% level of significance whether there is a relationship between smoking and visits to the physician. Status Visits to the Physician 0-1 2-4 >3D5 Smoker 25 60 75 Nonsmoker 110 90 40 The expected frequencies will be O a) 54, 44,81. 90 and 70 O b) 54, 60. 81. 90 and 69 Oc) 112, 100.90,81 and 69 Odi69.82. 55. 90 and 112
Which of these modelling techniques tends to use many small trees? O a. All of these O b. Decision Trees c. Random Forests O d. Gradient Boosting
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. This problem is an example of a Teens Adults Coffee 50 200 E!! Tea 100 150 Soft 200 200 Drink Other 50 50 Select one: O a. normally distributed variable O b. test for independence O c. binomial distributed variable O d. multinomial population
(6) At the top of the next page is a Bayes Net graph and four tables which characterize how four random variables interact to describe a single basketball shot: • D (defended): whether the player taking the shot was defended (D₁) or not (Do) while taking the shot. ● R (range): whether the player took a 2-point shot (R₂) or a 3-point shot (R3). ● M (made): whether the shot was made (M₁) or not (Mo). ● P (points): the points earned as a result of the shot, either 0 (Po), 2 (P₂), or 3 (P3).
Let A, B and C be events from a common sample space such that: P(A) = 0.72, P(B) = 0.56, P(C) =0.25, P(ANB) = 0.42. P(ANC) = 0.18, P(BOC) =0 %3D Compute P(AUBUC).
6. The following data are the weight gained in kgs of 15 dairy calves, grouped by cage, fed with 5 different brands of feed (T1, T2, T3, T4, T5) mixed with their feeds (kg). The experiment was conducted in RCBD. The calves are grouped into three cages as blocks. Treatment Blocks II T1 2.8 5.8 5.3 T2 2.7 3.6 3.5 T3 2.8 2.5 2.1 T4 3.2 3.8 3.5 T5 3.2 5.2 a. Coefficient of Variation (CV), b. Make a Decision 5323
Casinos are required to verify that their games operate as advertised. American roulette wheels have 38 slots-18 red, 18 black, and 2 green. In one casino, managers record data from a random sample of 200 spins of one of their American roulette wheels. The table displays the results. Color Count Red 85 Black 99 Which are appropriate hypotheses for testing whether the distribution of outcomes on this wheel is not what it should be? Green 16 Ho: Pred = : 94.7, Pblack = 94.7, Pgreen = 10.5 Ha at least two of the pi's are incorrect Ho: Pred 85, Pblack = 99, Pgreen = 16 Ha at least two of the pi's are incorrect Ho: each color is equally likely to appear Ha:each color is not equally likely to appear Ho: Pred = 18 38⁹. Pblack Ha at least two of the p;'s are incorrect = 18, green 38⁹ = 2 38 Ho: The distribution of outcomes is what it should be (the wheel is fair). Ha: The distribution of outcomes is not what it should be (the wheel is not fair).
A group of AP Statistics students wanted to see if plain, peanut, and almond M&Ms have the same color distribution. To test this, students took a random sample of each type of M&M and classified the candies in the sample by color. They plan to carry out a chi-square test to decide if there is evidence that the color distributions are not the same for the three types of M&Ms. Red Blue Green Orange Brown Piain 20 18 15 10 14 12 Peanut 8 6 8 25 5 7 Almond 7 11 10 12 10 What is the expected count for green peanut M&Ms? А 25/47 (25x47)/47 (59x47)/59 (59x47)/207 В C D
3. An experiment is studied to see whether the travelling time depends either on the routes (Factor A) or the days of the week (Factor B) and the travelling time was recorded and given below. Route (A) 1 2 3 4 1 22 25 26 26 Days of the week (B) 2 3 4 5 26 25 25 31 27 28 26 29 29 33 30 33 28 27 30 30 The two-factor random effects ANOVA model is given by Xij = μ + ai + Bj + € ij where μ is the true grand mean, a; is the effect of factor A at level i and ß, is the effect of factor B at level j. (a) State the assumptions required for the ANOVA model. (b) Create an interaction plot and comment on it. (c) Fit the model using R/Minitab and construct the ANOVA table. (d) State and test hypotheses appropriate for deciding whether routes has any effect on travelling time with a = - 5%. (e) State and test hypotheses appropriate for deciding whether days of the week has any effect on travelling time with a = 5%.
2.3

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1. [25 pts] Here is a plate model. A Obiect1 B E F Object2 a. What probability distributions do we need to specify for this model? b. Draw an unrolled version of the Bayesian network, where there are three items of type Object1 and two items of Object2 type.